파이썬통계14_가설과검정.ipynb

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      "cell_type": "markdown",
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      "source": [
        "# 추정\n",
        "* 보통 어떤 집단(모집단)의 특징을 알고싶다 => 전수조사\n",
        "\n",
        "* 현실에서는 시간/비용상의 문제 때문에 모든 구성원 대상 조사는 어려움 \n",
        "  + => 표본 이용(일부조사)\n",
        "\n",
        "* 알고자 하는 모집단의 특징을 숫자로 표현\n",
        "  + => 모수(평균,분산,비율, 표준편차)\n",
        "\n",
        "* 표본으로 뽑은 데이터 - 통계량, 추정치\n",
        "* 표본의 통계량을 \"'모수'가 이럴것이다\"라고 추리 => 추정\n",
        "\n",
        "\n",
        "* ex) 한국 성인 남자의 평균 키 파악\n",
        "  + 모집단 : 한국 성인 남자\n",
        "  + 모수 : 평균\n",
        "  + => 한국 성인남자 모두를 조사할 수 없으니 표본(남자 1000명)을 선정해서 평균을 구함\n",
        "  + => 표본의 평균으로 모집단의 평균을 추리함  \n",
        "\n",
        "* 추정은 일부 데이터로 전체를 추리하기 때문에 100% 정답은 아니고, 일부 오차는 존재함\n",
        "* 추정에는 점추정, 구간 추정이 있음"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nlelClLsczYq",
        "colab_type": "text"
      },
      "source": [
        "# 점추정\n",
        "* 추정치를 하나의 값(점)으로 표현\n",
        "* 성인 남자 평균 키 - 172.38cm(통계량)\n",
        "* 그런데, 진짜 한국 남성의 평균키가 172cm일까?\n",
        "  + 당연히 그럴 확률은 희박 => 표본수 작음, 오차 존재\n",
        "  + 따라서, 특성상 점추정은 신뢰하기 어려움\n",
        "\n",
        "* ex) 서울 지역내 하이마트에서 UHD TV를 구매한 고객의 평균 나이 추정\n",
        "* 경주를 방문한 관광객들의 평균 지출액 추정\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TlCITaNKdRwK",
        "colab_type": "text"
      },
      "source": [
        "# 구간 추정  \n",
        "* 추정치를 일정구간으로 설정\n",
        "* 즉, 신뢰도(신뢰수준)를 제시하면서 상한값과 하한값으로 추정\n",
        "\n",
        "* 성인 남자 평균 키 - 172.38cm(통계량) => 167 ~ 177cm (+-5)\n",
        "* 이렇게 하면, 이 구간에 모수가 포함될 확률이 높아짐\n",
        "* 추정치의 신뢰도를 높이고, 점추정치의 한계를 \n",
        "극복하기 위해 구간 추정을 사용함\n",
        "\n",
        "* ex) 서울 지역 IT노동자의 연간 평균 급여가 200만원이다 \n",
        "   + (점추정 - 신뢰도 하락)\n",
        "\n",
        "* 서울 지역 IT노동자의 연간 평균 급여가 180 ~ 220만원 사이에 있을 가능성이 85%이다 \n",
        "  + (구간추정 -어느 정도 신뢰도 보장)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YQqqRLlEd84W",
        "colab_type": "text"
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      "source": [
        "# 신뢰구간\n",
        "* 점추정은 특성상 신뢰도가 떨어짐 => 구간추정으로 보완\n",
        "* 그러면, 구간추정시 어느정도까지 구간을\n",
        "설정해야 할까?\n",
        "\n",
        "* 성인 남자 평균 키에 대한 구간추정을\n",
        "150~190으로 잡으면? => 너무 넓음\n",
        "  + 구간설정이 짧을수록 좋을까? 너무 짧아도 문제\n",
        "\n",
        "* 너무 넓지도, 짧지않게 나름의 기준에 따라\n",
        "신뢰가능한 구간을 설정 - 신뢰구간 사용\n",
        "\n",
        "* 주어진 확률로 모집단의 모수가 존재할 것으로\n",
        "예상되는 값의 범위 - 신뢰구간\n",
        "  + 이때, 주어진 확률은 '신뢰수준'이라 함\n",
        "\n",
        "* 신뢰수준 - 표본으로부터 계산한 결과에 대해 \n",
        "확실성 정도를 표현하는 것으로, 추정값으로 모수를 맞출 확률을 의미\n",
        " + 90% ~ 99.9% 정도로 표현"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-my8t3Ybe9ac",
        "colab_type": "text"
      },
      "source": [
        "# 추론통계의 두 갈래\n",
        "* 모집단으로부터 표본을 추출해서 모집단의 특성을 나타내는 모수에 대한 여러 가지 정보를 얻음 : 추론통계\n",
        "* 통계적 추론 = 추정 + 가설검정"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QUlomf-OfNuA",
        "colab_type": "text"
      },
      "source": [
        "# 가설검정\n",
        "* 추론 통계학에서 중요하게 여기는 3가지\n",
        "* 1. 표본집단은 모집단을 대표할 수 있나?\n",
        "  + 표본의 특성이 모집단을 잘 반영해야 함 -> 대표성을 지녀야 함\n",
        "  \n",
        "* 2. 표본의 확률분포는 어떤가?\n",
        "  + 어떤 분포이냐에 따라 추정을 위한 기법이 다름\n",
        "  + 단, 표본의 수가 많아지면 정규분포에 근사\n",
        "    \n",
        "* 3. 추정된 결과는 신뢰할 만 한가?\n",
        "  + 추정된 결과를 활용할 지 결정하는 요소"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qyFTrMfTg67d",
        "colab_type": "text"
      },
      "source": [
        "# 통계적 가설검정\n",
        "* 세상에는 수 많은 분야에 걸쳐 다양한 이론/관념이 존재\n",
        "* 이러한 이론/관념들은 그 자체로 정답이라기 \n",
        "보다는 '이럴것이다'라는 하나의 가설에 불과\n",
        "* 정답은 아니고 가설이므로 항상 불완전함이 내포\n",
        "\n",
        "* 한편, 불완전함을 채우기 위해 새로운 가설이 등장하기도 함\n",
        "* ex) 우주에 대한 가설\n",
        "  + 신화적 상상 -> 천동설 -> 지동설\n",
        "\n",
        "* 그런데, 새로운 가설이 이전가설보다 늘 합리적이고 신뢰적일까? \n",
        "* 오히려 이전 가설이 더 합리적일수도 있음\n",
        "\n",
        "* 따라서, 두 가설중 어떤 가설이 더 신뢰성있고 정확한지 판단해야 할 필요가 있음\n",
        "  + => 이 과정을 가설검정이라 함"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9DQZE07vhiHw",
        "colab_type": "text"
      },
      "source": [
        "# 통계적 관점의 가설\n",
        "* 검정을 전제로 모집단의 모수에 대한 진술 또는 가정\n",
        "\n",
        "* ex) 하이마트에서 일하는 모든 종업원의 평균임금은 200만원이다 - 가설\n",
        "\n",
        "* 이 가설이 옳은지 알아보기 위해서는 모든 영업점을 다 돌아봐야 함 - 사실상 불가능\n",
        "  + => 일정 수의 표본을 추출해서 표본 통계량을 조사하고 결정규칙에 따라 가설을 채택하거나 기각할 수 있음\n",
        "\n",
        "* 표본 통계량 조사 후 :\n",
        "  + 1) 표본평균 100만원 -> 가설기각\n",
        "  + 2) 표본평균 196만원 -> 가설채택? 오차 허용여부는?\n",
        "\n",
        "\n",
        "### 통계적 관점의 검정\n",
        "* 가설이 타당성 있는 진술인지 결정하기 위해\n",
        "표본증거와 확률이론에 기반하여 수행하는 과정\n",
        "\n",
        "* 이러한 검정은 수학적 증명을 동반하지 않고\n",
        "받아들일 만한 확률적 증거만을 제공\n",
        "* 따라서, 해석능력, 경험이 어느정도 동반되어야 함\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wB8wXIOqiOZK",
        "colab_type": "text"
      },
      "source": [
        "# 가설검정의 6가지 절차\n",
        "* 귀무/대립가설 설정 -> 유의수준 선정 -> 검정 통계량 선택 -> 결정규칙 수립 -> 표본추출, 결론도출 -> 결과 해석\n",
        "\n",
        "### 1. 귀무/대립가설 설정\n",
        "검정하고자 하는 가설을 설정\n",
        "\n",
        "* 귀무(null)가설 $H_0$\n",
        "  + 수치증거를 검정하기 위한 목표로 만들어진 모집단 모수값에 대한 진술(가정)\n",
        "\n",
        "* 대립(alternative)가설$H_1$\n",
        "  + 표본 데이터 정보로 귀무가설이 거짓이라는 충분한 증거를 제시할 때 채택되는 진술\n",
        "\n",
        "* ex) 상업적 항공기의 평균수명은 25년인지 알고 싶다\n",
        "  + 귀무가설 : 평균수명은 25년이다 (=)\n",
        "  + 대립가설 : 평균수명은 \n",
        "    25년이 아니다/25년이상/25년이하(>,<,!=)\n",
        "\n",
        "\n",
        "### 2. 유의수준 선정\n",
        "* 귀무가설을 기각하게 되는 확률\n",
        "  + 일반적으로 소비자 관련 - 0.05\n",
        "  + 품질보증 관련 - 0.01\n",
        "  + 정치 여론 조사관련 - 0.10\n",
        "\n",
        "* ex) 전자회로기판PCB 생산업체에서\n",
        "불량률이 6% 이하일때 계약업체로 선적해서\n",
        "납품한다는 품질보증계약 체결함\n",
        "\n",
        "  + 귀무가설H0: 불량률 6% 이하 - 선적 o\n",
        "  + 대립가설H1: 불량률 6% 초과 - 선적 x\n",
        "\n",
        "  + 4000개의 회로판에서 표본 50개 추출 \n",
        "    + -> 4개가 불량 -> 0.08 -> 8% -> 선적x\n",
        "    + 그런데, 4개의 불량이 전체 4000개에서 유일하다면? \n",
        "    + => 불량률 0.1% -> 선적취소는 잘못된 결정\n",
        "    + => 귀무가설이 옳지만 기각했음 (제1종오류(알파$\\alpha$))\n",
        "\n",
        "  + 4000개의 회로판에서 표본 50개 추출\n",
        "    + -> 2개가 불량 -> 0.04 -> 4% -> 선적o\n",
        "    + 그런데, 48개 정상품이 전체 4000개에서 유일\n",
        "    + -> 불량률 98.8% -> 선적허용은 잘못된 결정\n",
        "    + => 귀무가설이 틀리지만 기각못함 (제2종오류(베타$\\beta$))\n",
        "\n",
        "\n",
        "### 3. 검정 통계량 선택\n",
        "* 귀무가설을 기각할 것인지를 결정하기 위해서 표본으로부터 계산된 값\n",
        "\n",
        "* 일반적으로 z검정값, t검정값등을 사용\n",
        "* 상황에 따라 F/카이제곱 검정값도 사용\n",
        "\n",
        "### 4. 결정규칙 수립 - 단측/양측 검정\n",
        "* 귀무가설이 기각될 특정 조건과 기각되지 않을 조건을 명시\n",
        "* 일반적으로 기각영역은 귀무가설이 발생할 가능성이 없도록 작게 설정\n",
        "\n",
        "* 단측검정 : one-side, 한쪽 꼬리 검정\n",
        "  + 방향성(크다/작다)이 대립가설에 포함되는 경우 시행하는 검정\n",
        "\n",
        "* 우측(오른쪽) 단측검정\n",
        "  + ex) 농심의 '오징어다리' 스낵의 포장중량이 500g미만인지 검정한다고 가정\n",
        "\n",
        "  + 귀무가설 : 포장중량이 500g미만\n",
        "  + 대립가설 : 포장중량이 500g이상\n",
        "  + 유의수준 0.05일때 귀무가설이 기각될 영역(기각역)은 \n",
        "임계값 1.645 기준 오른쪽 영역\n",
        "  + 임계값 : 귀무가설을 채택하거나 기각할 영역 사이의 분기점\n",
        "\n",
        "* 좌측(왼쪽) 단측검정\n",
        "  + ex) 현대 자동차에 장착되는 타이어의 평균 수명이 50000km 이상인지 검정\n",
        "\n",
        "  + 귀무가설 : 평균 수명이 50000km 이상\n",
        "  + 대립가설 : 평균 수명이 50000km 미만\n",
        "\n",
        "  + 유의수준 0.05일때 귀무가설이 기각될 영역(기각역)은 \n",
        "임계값 -1.645 기준 왼쪽 영역\n",
        "\n",
        "* 양측검정 - two sided, 양쪽 꼬리 검정\n",
        "  + 방향성(크다/작다)이 대립가설에 포함되지 않는 경우 시행하는 검정\n",
        "\n",
        "  + ex) 회계사의 연평균 수입은 5500만원인가?\n",
        "  + 귀무가설 : 연평균 수입은 5500만원 이다\n",
        "  + 대립가설 : 연평균 수입은 5500만원 아니다\n",
        "\n",
        "  + 유의수준 0.05일때 귀무가설이 기각된 영역은 임계값 -1.96(0.025)/1.96(0.025) 기준 양쪽 영역임\n",
        "\n",
        "### 5. 결론도출 \n",
        "* 만약, 계산된 검정 통계량 z값이 기각역을 넘는 값이라면 (ex: 2.34) 귀무가설은 기각됨\n",
        "\n",
        "* 계산된 검정 통계량 z값이 기각역을 넘지 않는 값이라면 (ex: 0.71)\n",
        "귀무가설은 채택됨\n",
        "\n",
        "* 하지만, 1종오류/2종오류가 발생할 수도 있음\n",
        "\n",
        "* 유의확률 p-value\n",
        "  + 귀무가설이 참이라고 가정할때 주어진 데이터가 관측될 확률\n",
        "  + 또는 극단적인 데이터가 관측될 확률을 의미\n",
        "  + 따라서, '유의확률이 유의수준보다 작으면 귀무가설을 기각할 수 있음' (중요!)\n",
        "\n",
        "![](https://github.com/siestageek/bigdataset/blob/master/t-table-1.png?raw=true)\n",
        "\n",
        "\n",
        "\n",
        "### 6. 결과 해석\n",
        "* 통계를 이용해서 가설검정이 모든 분야의 가설을 다 판단하지 못함\n",
        "* 수학적 특성상 제약이 존재(표본의 편중)\n",
        "* 판단의 의사결정시 수학적 방법을 이용하는 것도 좋지만, 수학의 틀에서 벗어나 의사결정하는 것도 좋음\n",
        "  + => 동물적 직감, 영감을 이용\n",
        "\n",
        "* 즉, 참/거짓이 존재하는 수학적 가설과는 달리 통계적 가설은 참/거짓의 유무보다는 확률만 존재함 \n",
        "  + 언제나 틀릴 가능성 내포\n",
        "\n",
        "* ex) 회계사의 연평균 수입은 5500만원인가?\n",
        "  + 귀무가설 : 연평균 수입은 5500만원 이다\n",
        "  + 대립가설 : 연평균 수입은 5500만원 아니다\n",
        "\n",
        "  + 결론 : 연평균 수입은 5500만원 이다 (x)\n",
        "    + 연평균 수입이 5500만원일/아닐 \n",
        "       확률이 다소 높다/낮다 (o)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JChRgbpVuwRZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "outputId": "31763cc8-cd0b-40f9-d826-bf45c6bfbc8e"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy import stats\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IIAqrfuqux52",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 407
        },
        "outputId": "026f6f8d-74c1-4cec-a7a5-ff618a331124"
      },
      "source": [
        "# 가설검정 예\n",
        "# 성인의 평균키는 67.6인치(172cm)인지 알아보자\n",
        "# 귀무가설 : 성인의 평균키는 67.6인치 이다!\n",
        "# 대립가설 : 성인의 평균키는 67.6인치 아니다!\n",
        "# 검정방법 : 양측검정\n",
        "data = pd.read_csv('https://raw.githubusercontent.com/siestageek/bigdataset/master/coffee.csv')\n",
        "data"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>age</th>\n",
              "      <th>drinks_coffee</th>\n",
              "      <th>height</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>4509</td>\n",
              "      <td>&lt;21</td>\n",
              "      <td>False</td>\n",
              "      <td>64.538179</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1864</td>\n",
              "      <td>&gt;=21</td>\n",
              "      <td>True</td>\n",
              "      <td>65.824249</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2060</td>\n",
              "      <td>&lt;21</td>\n",
              "      <td>False</td>\n",
              "      <td>71.319854</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>7875</td>\n",
              "      <td>&gt;=21</td>\n",
              "      <td>True</td>\n",
              "      <td>68.569404</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>6254</td>\n",
              "      <td>&lt;21</td>\n",
              "      <td>True</td>\n",
              "      <td>64.020226</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2969</th>\n",
              "      <td>5984</td>\n",
              "      <td>&gt;=21</td>\n",
              "      <td>True</td>\n",
              "      <td>68.544084</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2970</th>\n",
              "      <td>5302</td>\n",
              "      <td>&lt;21</td>\n",
              "      <td>True</td>\n",
              "      <td>63.822921</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2971</th>\n",
              "      <td>5978</td>\n",
              "      <td>&gt;=21</td>\n",
              "      <td>True</td>\n",
              "      <td>67.298275</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2972</th>\n",
              "      <td>3900</td>\n",
              "      <td>&lt;21</td>\n",
              "      <td>False</td>\n",
              "      <td>60.095933</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2973</th>\n",
              "      <td>5705</td>\n",
              "      <td>&lt;21</td>\n",
              "      <td>False</td>\n",
              "      <td>63.765869</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>2974 rows × 4 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "      user_id   age  drinks_coffee     height\n",
              "0        4509   <21          False  64.538179\n",
              "1        1864  >=21           True  65.824249\n",
              "2        2060   <21          False  71.319854\n",
              "3        7875  >=21           True  68.569404\n",
              "4        6254   <21           True  64.020226\n",
              "...       ...   ...            ...        ...\n",
              "2969     5984  >=21           True  68.544084\n",
              "2970     5302   <21           True  63.822921\n",
              "2971     5978  >=21           True  67.298275\n",
              "2972     3900   <21          False  60.095933\n",
              "2973     5705   <21          False  63.765869\n",
              "\n",
              "[2974 rows x 4 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0XCa1X3gC6wC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "a600260d-c5d1-4dc8-b871-a630d382e8b0"
      },
      "source": [
        "# 단일표본 t검정 : ttest_1samp(표본, 평균)\n",
        "result = stats.ttest_1samp(data['height'], 67.6)\n",
        "\n",
        "# 대립가설 채택여부 확인/귀무가설 기각여부 확인 \n",
        "# p-value가 0.05보다 작은 경우 귀무가설 기각함\n",
        "result"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=-0.04393310841362738, pvalue=0.9649606744467513)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tmVsoSECD7zP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 90
        },
        "outputId": "89e69d24-d9de-4081-9dd2-ffd409bcd4a9"
      },
      "source": [
        "# 학생들의 키가 평균 175cm인가에 대한 가설검정\n",
        "np.random.seed(2007221450)\n",
        "heights = np.random.randint(low=162, high=182, size=50)\n",
        "print(heights, np.mean(heights))\n",
        "\n",
        "result = stats.ttest_1samp(heights, 175)\n",
        "print(result)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[174 168 173 163 173 170 175 163 173 178 172 163 166 171 172 165 165 164\n",
            " 172 163 163 179 168 169 177 176 181 168 180 170 180 176 168 173 179 178\n",
            " 173 173 179 163 174 171 172 172 162 171 168 170 181 168] 171.3\n",
            "Ttest_1sampResult(statistic=-4.779118408380455, pvalue=1.642785429705055e-05)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dp-SrkoUF43b",
        "colab_type": "text"
      },
      "source": [
        "# 두 표본 가설검정\n",
        "* 단일표본의 비교문제는 하나의 모집단에서 추출된 하나의 표본에 대해 검정\n",
        "\n",
        "* 그에 비해 두 표본 비교문제는 독립적(서로 관련없음)인 두 모집단으로 부터 각각 추출된 표본의 경우와\n",
        "* 동일한 모집단으로부터 추출된 두 표본의 경우로 나누어 검정을 실시함\n",
        "  + => 2개의 집단간의 차이가 의미 있는지 확인\n",
        "\n",
        "* 일상에서는 단일 표본문제보다 더 많이 사용됨\n",
        "  + ex) 남자와 여자간의 소득 차이 비교 (독립표본)\n",
        "  + 과외를 받기 전과 후의 성적 차이 비교 (짝 표본)\n",
        "\n",
        "### 정규성 검정\n",
        "* 데이터의 분포가 정규분포를 따르는지 알아보는 것을 의미\n",
        "* 통계의 다양한 검정법은 데이터의 정규분포를 가정하고 수행됨\n",
        "* 데이터가 충분히 크다면(보통 30개 이상) 중심극한정리를 적용할 수 있음\n",
        "* 하지만, 그 이하일 경우 별도의 정규성 검정이 필요할 수 있음\n",
        "* 독립표본을 이용해서 가설검정을 실시하기 위해서는   \n",
        "  반드시 정규성, 등분산성이 만족되어야 함"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qCNYVsedGEDR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "bedc0e39-bfd7-41d7-9082-c0559b54d3af"
      },
      "source": [
        "# 단일표본 정규성 검정\n",
        "# 표본의 수가 2000미만인 경우 shapiro-Wilks 검정 실시\n",
        "# pvalue가 0.05보다 크면 표본이 정규성을 띈다고 볼 수 있음\n",
        "samp = data['height'][:20]\n",
        "\n",
        "stats.shapiro(samp)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.9590533375740051, 0.5251146554946899)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "34FQW9sGJRam",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "89b3313d-5ba7-4df1-a9ae-700d3eabf36a"
      },
      "source": [
        "# 정규성 검정에 대한 시각화\n",
        "plt.boxplot(samp, vert=0)\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XeiGdBB_K-a7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "6bbf24b7-97f0-467c-f07f-e7799e3b48cb"
      },
      "source": [
        "# ex) 독립표본 x, y 에 대해 정규성을 확인하시오\n",
        "x = [175,168,168,190,156,181,182,175,174,179]\n",
        "y = [185,169,173,173,188,186,175,174,179,180]\n",
        "\n",
        "result1 = stats.shapiro(x)\n",
        "result2 = stats.shapiro(y)\n",
        "print(result1)\n",
        "print(result2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(0.9635064005851746, 0.8249932527542114)\n",
            "(0.9306508898735046, 0.454325407743454)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UvxzhHLMLfEn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "d2921401-1a0e-4495-e34d-8c5cfa6c785c"
      },
      "source": [
        "# 두 표본 등분산성 검정\n",
        "# 두 표본의 분산(표준편차)이 비슷한지 여부를 알아봄\n",
        "# levene 함수를 이용하거나 bartett 함수를 이용함\n",
        "# pvalue가 0.05보다 크면 표본이 등분산성을 띈다고 볼 수 있음\n",
        "result1 = stats.levene(x, y)\n",
        "result2 = stats.bartlett(x, y)\n",
        "print(result1, result2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "LeveneResult(statistic=0.2900626678603398, pvalue=0.5967786336494338) BartlettResult(statistic=1.1514189007733604, pvalue=0.2832523209020049)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eO0sSP0NQdSq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "f637b1c8-a3ab-4d93-e62e-81783666b8ee"
      },
      "source": [
        "# 독립표본에 대한 x,y에 대해 평균의 차이가 존재하는지 t검정\n",
        "# 독립표본 t검정 : ttest_ind(표본1, 표본2, 등분산성여부)\n",
        "# 만일, 등분산성 검정을 실패하는 경우 equal_var=False로 설정\n",
        "# p-value가 0.05보다 작은 경우 귀무가설 기각함\n",
        "# 귀무가설 : x,y에 대해 평균의 차이가 존재 않음\n",
        "# 대립가설 : x,y에 대해 평균의 차이가 존재함\n",
        "\n",
        "result = stats.ttest_ind(x, y)\n",
        "print(result)  # p:0.355 => 귀무가설 채택 => 평균차이없음"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ttest_indResult(statistic=-0.9473729613780933, pvalue=0.3559948666339564)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OzYlHfklUD2R",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "outputId": "a50e362a-394c-49ed-dfcf-cc6534b76d0d"
      },
      "source": [
        "# ex) 자동차 연비 데이터에서 기어 종류에 따라 \n",
        "# 평균 연비의 차이에 의미가 있는지 검정\n",
        "# 귀무가설 : 기어의 종류에 따라 평균연비의 차이가 존재 않음\n",
        "# 대립가설 : 기어의 종류에 따라 평균연비의 차이가 존재함\n",
        "mtcars = pd.read_csv('https://raw.githubusercontent.com/siestageek/bigdataset/master/mtcars.csv')\n",
        "auto = mtcars[mtcars['am'] == 0]['mpg']\n",
        "manual = mtcars[mtcars['am'] == 1]['mpg']\n",
        "print(auto[:12])\n",
        "print(manual[:12])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "3     21.4\n",
            "4     18.7\n",
            "5     18.1\n",
            "6     14.3\n",
            "7     24.4\n",
            "8     22.8\n",
            "9     19.2\n",
            "10    17.8\n",
            "11    16.4\n",
            "12    17.3\n",
            "13    15.2\n",
            "14    10.4\n",
            "Name: mpg, dtype: float64\n",
            "0     21.0\n",
            "1     21.0\n",
            "2     22.8\n",
            "17    32.4\n",
            "18    30.4\n",
            "19    33.9\n",
            "25    27.3\n",
            "26    26.0\n",
            "27    30.4\n",
            "28    15.8\n",
            "29    19.7\n",
            "30    15.0\n",
            "Name: mpg, dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ryTx3D3jVTBq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "c01bb8b7-45d8-4218-e3f3-f16d379c173a"
      },
      "source": [
        "# 추출한 데이터중 12개만 가져와서 정규성,등분산성 검정\n",
        "x = auto[:12]\n",
        "y = manual[:12]\n",
        "result1 = stats.shapiro(x)\n",
        "result2 = stats.shapiro(y)\n",
        "result3 = stats.bartlett(x, y)\n",
        "print(result1)\n",
        "print(result2)\n",
        "print(result3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(0.9817473292350769, 0.9896629452705383)\n",
            "(0.9455317854881287, 0.5728504061698914)\n",
            "BartlettResult(statistic=2.6617051044726785, pvalue=0.10279049078481733)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "42RdtStnWgAP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "e7ce1113-acc6-431a-99d9-42745ce74f2e"
      },
      "source": [
        "# 독립표본 t검정 시행\n",
        "result4 = stats.ttest_ind(x, y)\n",
        "print(result4)\n",
        "# p-value값이 0.05보다 작기때문에 귀무가설 기각\n",
        "# => 기어유형에 따라 평균연비의 차이가 존재할 확률이 높음"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ttest_indResult(statistic=-3.0985072529588464, pvalue=0.005243381009039916)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qH8HPWYcIivL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "dab100a5-7a7a-4f5f-a16c-190d4e61d6f3"
      },
      "source": [
        "# 연비 데이터 갯수 수정없이 바로 독립표본 검정 실시\n",
        "mtcars = pd.read_csv('https://raw.githubusercontent.com/siestageek/bigdataset/master/mtcars.csv')\n",
        "auto = mtcars[mtcars['am'] == 0]['mpg']\n",
        "manual = mtcars[mtcars['am'] == 1]['mpg']\n",
        "\n",
        "# 정규성, 등분산성 검정\n",
        "result1 = stats.shapiro(auto)\n",
        "result2 = stats.shapiro(manual)\n",
        "result3 = stats.bartlett(auto , manual)\n",
        "print(result1)\n",
        "print(result2)\n",
        "print(result3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(0.976774275302887, 0.8987362384796143)\n",
            "(0.9458035826683044, 0.536271333694458)\n",
            "BartlettResult(statistic=3.2258823148923645, pvalue=0.07248272665325972)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y7xOk0-wJ1_e",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "5c704d09-b9cb-447e-ddfd-9dfbe8a19cbf"
      },
      "source": [
        "# 독립표본 t검정 시행\n",
        "result4 = stats.ttest_ind(auto, manual)\n",
        "print(result4)\n",
        "# p-value값이 0.05보다 작기때문에 귀무가설 기각\n",
        "# => 기어유형에 따라 평균연비의 차이가 존재할 확률이 높음"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ttest_indResult(statistic=-4.106126983100689, pvalue=0.0002850207439350686)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X1xiPtcYJ_0K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# ex) 잔디 깍기 기계 생산 공장에서 작업시간 단축을 위해 2가지 공정이 제안되었음\n",
        "# A 공정방식은 5명의 근로자에 의해, B 공정방식은 6명의 근로자에 의해 \n",
        "# 각각 테스트가 진행되었을때, 작업시간의 차이가 있는지 검정하시오. \n",
        "# 유의수준 0.10을 사용한다\n",
        "# A 공정 : 2 4 9 3 2 (단위: 분)\n",
        "# B 공정 : 3 7 5 8 4 3\n",
        "\n",
        "# 귀무가설 : 각 공정방식에 의한 평균 작업시간의 차이가 없다\n",
        "# 대립가설 : 각 공정방식에 의한 평균 작업시간의 차이가 있다\n",
        "# 독립표본 t검정시 자유도df : (n1-1) + (n2-1)\n",
        "\n",
        "a = [2,4,9,3,2]\n",
        "b = [3,7,5,8,4,3]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kN_QyrBmKKD2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "54fc4738-ade7-4b15-be25-fef8b7ec660f"
      },
      "source": [
        "# 정규성과 등분산성 검정\n",
        "result1 = stats.shapiro(a)\n",
        "result2 = stats.shapiro(b)\n",
        "result3 = stats.bartlett(a, b)\n",
        "print(result1)\n",
        "print(result2)\n",
        "print(result3)\n",
        "# a 표본은 정규성을 확실하게 띈다고 보기에 어려울 수 있음"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(0.7755950689315796, 0.05049796402454376)\n",
            "(0.8904140591621399, 0.3203631043434143)\n",
            "BartlettResult(statistic=0.4356449209175901, pvalue=0.509231991519868)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TNhGKu3OLR2T",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "95988613-4321-485e-f8cb-97fb0708d898"
      },
      "source": [
        "# 독립표본 t검정실시\n",
        "result4 = stats.ttest_ind(a, b)\n",
        "print(result4)\n",
        "# p-value값이 0.05보다 크기때문에 귀무가설 채택\n",
        "# => 공정방식에 의한 평균 작업시간의 차이가 없다"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ttest_indResult(statistic=-0.6620511221285622, pvalue=0.5245263510606547)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rhQYhtlLNW78",
        "colab_type": "text"
      },
      "source": [
        "# QQ plot\n",
        "* 통계추론은 대부분 모집단이 정규분포를 따른다는 가정하에서 진행됨\n",
        "* 수집데이터를 표준 정규분포의 분위수와 비교해서 그리는 그래프\n",
        "* 데이터가 정규성을 띈다면 직선에 가까운 형태로 그려짐\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O8_BIfn0NWLj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 443
        },
        "outputId": "b8328b1f-7eea-4c06-910c-9a27696edea1"
      },
      "source": [
        "np.random.seed(2007231000)\n",
        "\n",
        "n = 100\n",
        "x1 = np.random.normal(0,1, n) # 정규분포를 따르는 난수\n",
        "x2 = np.random.exponential(2, n) # 지수분포를 따르는 난수\n",
        "x3 = np.log1p(x2) # 지수분포난수를 로그화함\n",
        "\n",
        "f, ax = plt.subplots(2,3, figsize=(12,6))\n",
        "ax[0][0].boxplot(x1)\n",
        "stats.probplot(x1, plot=ax[1][0])  # qqplot\n",
        "\n",
        "ax[0][1].boxplot(x2)\n",
        "stats.probplot(x2, plot=ax[1][1])  # qqplot\n",
        "\n",
        "ax[0][2].boxplot(x3)\n",
        "stats.probplot(x3, plot=ax[1][2])  # qqplot\n",
        "\n",
        "print(stats.shapiro(x1))\n",
        "print(stats.shapiro(x2))\n",
        "print(stats.shapiro(x3))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(0.9927886724472046, 0.8749861121177673)\n",
            "(0.8625355362892151, 3.545775939528539e-08)\n",
            "(0.9423452019691467, 0.0002687772794160992)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 6 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xi3kITnkQqSE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "eafd116f-ac0f-4c78-cb3f-8a77c3533750"
      },
      "source": [
        "sns.distplot(x1, fit=stats.norm)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f255c5cfe80>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "izXAchrORHu-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "b2f6a8f6-a30c-459d-f1ce-2e15548bba7a"
      },
      "source": [
        "sns.distplot(x2, fit=stats.norm)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f255c674b70>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uWcSA29fRJhS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "c19f33aa-373a-4969-9cab-154aed467e3f"
      },
      "source": [
        "sns.distplot(x3, fit=stats.norm)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f255c645f98>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pMJiA730SI2J",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "20c96016-b360-4a56-da39-462313b9b50a"
      },
      "source": [
        "sns.distplot(a, fit=stats.norm)\n",
        "sns.distplot(b, fit=stats.norm)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f255c79c518>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ybtw41qxZQ1hYWLm9rxCmkkAvSmVj0GXsrAxlPm1zTSOHNDysM9ke53zTvS2BQcRdTWFE3wCz7Zk31WOPPYatrS1z584t1/cVwhQS6MUt01qz8eRlujWsjq1V+UyTWCjo6pbI0USH6/bUZ2Rm88e2IzT186RZvZLnsiktNzc3HnzwQdatWydJz0SlI4Fe3LITFxO5eDWdvs3K93zXrm6JaBQ7843qtx08TWJyGvf2alvuo/lrHn74Yezt7fnyyy8r5P2FKIwEenHLNgZdRinoXUYPSRXGxy6TevZp7MgL9NnZOazbeZRGtWvSuG7ZbvEsiqurK+PHj+fvv//m/PnzFdYPIW4kgV7css2nrtDa15Xqjjbl/t5d3RIJS7UjIs2a3cdCibuawuDurcu9HzcaP348lpaWfP+9PAQuKg8J9OKWxKVkcjTyKj0aVUxa6S5uiSg022McWbP9CLVrudOiofnz7JRUjRo1GDZsGKtWrSI2NraiuyMEIIFe3KIdITFoDd0rKNC7WuXQwjmFbScuEhVzlUHdWlbY3PyNHnnkETIyMli0aFFFd0UIQAK9uEXbg6NxsbOilY9rhfWhY7UkkoN34+LsSECzWz9QxNzq1atHnz59WLx4MampqcVXEKKMSaAXJaa1ZtuZaLo2qI7BouJG0Z7p5zDEhFKraXsMhsr1o/zoo49y9epVfv3114ruihAS6EXJBV9O5nJiBt0als9DUoXZvf8YymBFlGeXWz5msKy0bduWNm3a8MMPP5CTk1PR3RF3OAn0osS2Bece4F5R8/MAiclp7D4aQoNm/kRpVyLSrSusL4WZMGECkZGRbN26taK7Iu5wEuhFiW07E02DGo54uZrv1KaS2rw/iOwcIyO7Nkah2RN/c+6bita7d29q1qwpZ8uKCieBXpRIelYOe8/G0b1hxY3ms7Jz+Gd/EC0b+tDY04nGjmnsrYSB3srKijFjxrBz507Onj1b0d0RdzAJ9KJE9p6NIzPbSLdGFTc/v/9EGInJafTr2ByAu1yTuJBuy8VKOH0zatQorKysWLJkSUV3RdzBJNCLEtkWHI21pQUd/dwrrA9bAk9T080Z//reAHSolgRQKUf11atXZ8CAAfz2229y3KCoMBLoRYlsC46mQ1037KzLJ1vljS5GJxB8Poru7RpjIAfn5DD8k3bxvt1CWsT9jWf0DqolnsI6K7FC+leQcePGkZyczB9//FHRXRF3KEtTCimlBgKfAQbgO631zBvudwc+BVoCY7XWK/LdywGO5b0M11oPNUfHRfm7nJjOmSvJjGxXcakGth04jcFC8UCNYOqfWoNBZwPgqy0wAlZXjP+WTbSsToJbS6KrtQHcKqbD5B432KxZMxYtWsSYMWMqzRO84s5RbKBXShmAuUA/IALYr5RarbU+ma9YOPAw8GIBTaRprSs+25Qotd2hublbOtevmPl5lRrL7gPH6O2VRp3sK2yNr8G6MNgTkUNsugUahb2lkQbO2QR4ZNLbO5F22ZvwjNrM6TON8Gh/L24e5Z/dUinFuHHjeP311wkMDKR9+/bl3gdxZzNlRN8BCNFahwEopZYCw4B/A73W+lzePWNBDYiqYXdoLM62ljTzuvl0p7JWPeEIQXs2cjXDBRtLCzqvdEdZ2dDUz5M+3Wvg6eHK91ca4GhjwajakSSlpLMhLpE/w8NpZzjFQM/TZO78kNVX/fDtOIw2jeuUa//vuecePvjgA5YvXy6BXpQ7UwK9N3Ah3+sI4K4SvIetUioQyAZmaq1X3VhAKTURmAhQu3b5nfUpSmZ3WCx31XMv37QH2oh3xBp8Eg/xclB1DEpz2aExT41rQlM/r+tSH3R0dGZ1lDvVqmfiW8tIs/reQFNgABHGGLKO/sZQ9zCC93/Bfze0ZPyIQfh5ls+isp2dHYMHD2blypVMmzYNV9eKyxEk7jzlsRhbR2sdAIwDPlVK1b+xgNb6G611gNY6wMOj4vZni8JFxKcSHpdKp3rluNsmJwu3Ez/ik3iIWUecOBlvTd9OLXh6TF+aN/C5Kb9NgGsyRhSHrjre1FTd+o1oOPwVMlo9jI+LJS/5HmTZ/M+Z8dMGUtIzy+XjjB49mszMTFmUFeXOlEAfCfjme+2Td80kWuvIvH/DgC1AmxL0T1QS1+bnO9Uvn0CflJSMYc9XNFQX+CbUk1N27VBKMaBTi0Lr1LdPx9Uym/0JNwf6a2x8W2Pf/zWURxOmtr5K94yNPPLOdxwLu1QWH+M6TZo0oUWLFvzyyy/oypacR1RppgT6/UBDpZSfUsoaGAusNqVxpVQ1pZRN3vfVgS7km9sXt4/dYbFUs7eicc2y36t++uwl0nd9S4BrAn+lt6bp3Y9w9MwFWjXyxc3FodB6FgrauSZzJNGBLGMR00s2Tlh3egJajKKLVw5ftA3jnc++55vVezAayzYAjxo1ipCQEA4fPlym7yNEfsUGeq11NjAZWA8EAb9orU8opaYrpYYCKKXaK6UigFHAPKXUibzqTYFApdQRYDO5c/QS6G8zWmv2hMbSsZ47FmU4P6+1Zve6FSTuX8pgnyRO2LWnWruhHDsTQWJyGj3aNS62jQDXJNKNBk4k2RddUCmo0wWLLs/g4erA4j4xnNqznufm/E5aRpaZPtHN7rnnHuzt7Vm+fHmZvYcQNzJpjl5rvVZr3UhrXV9rPSPv2pta69V53+/XWvtorR201u5aa/+867u01i201q3y/p1fdh9FlJXwuFQuXk0v02kbozGHv36ei3H750z2TyLKsTnJfgMB2HrgFK5O9rRs6FtMK9DcKRUbCyOBBczTF8jVF4vuL2LlXodPOsfjnxHII+8tITohuTQfp1AODg4MHjyYdevWkZhYeR7qElWbPBkrivXv/HwZLcRmZ2aycu4Mruz7jY+7JpNs60m471BQitiEZI6FRNCtbSOTDhexttC0dE7hQIKj6TnqbZxQnZ6G2p2Y2DSZp32DePTdHzl7qWzOfB09ejTp6en8+eefZdK+EDeSQC+KtTssluqONjSoYeIouQQy09NYNGsaIQd38M0gKwxWtpzxHY22yN35u+3gaQC6ty1+2uaa9q5JxGVZEZZqa3pHLCyh5RhoMYqutTL4ov05ps3+iZDImBJ9HlP4+/vTrFkzWZQV5UYCvSiS1prdobF0rOdm9kf3MzPSWTL7DS6cOcHnDzanDpHsbf42mdYuABiNRrYfDMa/vg8e1UxfBG7jkoJCc8DU6Zv86nRBdXoKXxdLvul0gTnzFhB8Ibrk7RRj1KhRnD59mmPHjhVfWIhSkkAvihQWk8KVpAyzpz3Iysxg2advcSH4BE8/OoYeGf8Q6jOcC579/y1z9EwEcYkpJi3C5udsmUMTx7Qit1kWyb0Bhh4vYuNcnVntL7Jm8dcEh1+5tbYKMXjwYOzs7GRRVpQLk5KaiTtXWeyfz8nOYvnn73Du1BHue/w5xhu/Js3Wg4NNXrqu3NYDp3F2sKVN45I/Ld3ONZmFETW4kmFFDZtb2EVj7451jxdI3fM9z/mfYs3aOdjfOwWfwO9L3lYBHIG72zdg7R+/M7W/Nw52NqVvNOCR0rchqiQZ0Ysi7Q6LpZazLXXdi9muaCJtNLJ6/ieEHj/AkEeeY0yNMFyTQ9jv/yZZVv+bnklISuVIcDhd2zTC0rLkKZHbu+TmqL+l6ZtrLG2w7zKR2JpdGeSTyNV/ZhEXffnW27vByJ4tSc3IYu3eU2ZrU4iCSKAXhbq2f75TfXezzc//s2IBx3dvovfIR+kS4I9/2Hec87ybizW6X1du+8FgjEZN9xJO21xTyzYLH9sMAm91+uYaZYF7+5Gc9RxCPYd0jNs+JvVyaOnazNO6gRf1vd1ZseWoWdoTojAS6EWhgi8nE5uSabZtlfs2rGL32uUE9B5C50GjaXvqY4zKwKEmL1xXzmjUbDt4mqZ+ntRyd7nl9wtwTeJkkj3J2aX/Mfdr14eT3mPIyjFivW8OOaFbMX3/ZsGUUozq2YqjoZfKZMFXiGsk0ItC7Q7N3Vpojvn54MN7WL/4axq37cyABybhGbsb38v/cKL+RNJsa15X9mRYJNHxSfRo16RU79nOJTfJ2eFE82wLbde+I3vdR7HjkjWGoN/gwPeQlVqqNod28cfK0iCjelGmJNCLQu0Oi8Xb1Q5ft9LNz1+JPMdvX8/Es04Dhj/xCgaMtDv5AUn2vpyq+9BN5bceOI2DnQ1tm5YuZ3wDh9wkZ6Wevsnn3j4d2ePQnw8PO2OMOgbbPobYW5/KqeZkR7+AhqzeeYKMzGyz9VOI/CTQiwIZjZq9Z+NKPZpPTU7kl0/fxtrGjtFT3sLKxpZG55fgkhLGgaavYDRYX1c+JTGBg6fO06V1Q6ytSrcp7FqSs8NXHcjIKVVT13np/l6E2bXkwX/cScvKgd1z4MRvkHNr6Y5H9WzF1ZR0NgQGm6+TQuQjgV4UKCgqkYTUrFLNz+dkZ7Ny7n9JjI9h9JS3cHbzwCYjjhYhX3HRoysXPbrfVOfozg3k5BhLvHe+MO1ckkgzGtgbbV18YRMZLCyY9dQQEm28uOdPN1JqtoezW2H7xxB3tsTtdWhaG98arizfcsRsfRQiPwn0okDm2D+/acUCzgUdYfAjz+JdP3e+3T/sOyyzU3P3zN+wk0drzcGtf9Gwdk28a1S79c7n08I5N8nZhkvmC/QADnY2fP7MvSRlaB7+I5vMdhMhOxN2fQZHlkJmisltWVgoRvZoyb6gC5yLijNrP4UACfSiEHvCYqnrbo+Xq90t1Q8K3MGev1YS0GcILbv0BcA+7RINzy/lrM8wEh3r3VQn/PQx4qIizDaah/8lOdtw0aa0m2Ru4ufpxswnBnH8bBT/XRsOPV+Fer0hYh9seQ/C94A27Rjle7s3x2ChWLlVUiII85NAL26SnWNkb9itz8+fPXuW1d/NwqteY/qNnfjv9RZnvgSlONZgUoH1Dm5dh42dA+39b/4lUBrtXZOISjNwLN78D4L3DWjIxCEdWb7lKCt2nIZmQ6HbS+BYE44uhe2zIPp0se3UcHWkZ+v6rNp+nKxsMy4oCIEEelGAExcTScrIpuMtzM+npaXx7LPPYrC0ZOTTr2NplTtl4pwchl/kaoJrjyXVzvPmesmJBO3fTovOvbGxNm9AbuuSjEFp/r5ohjQDBZgysiud/Ovw7k8bOB52CZw9odP/QduHIDsd9n4Fe+dBYtHHFY7s1YqYqylsOWyeB7KEuEYCvbjJ7rBbyz+vteadd97hzJkzDH9yKi7uNf691zL4C3IMdpys/3iBdY/t3kROdhZtetx96x0vhJOlkQ7Vs8os0BssLJj19BDcnR2Y8vnvJCSn5a4/eLWFHq9C02GQcA62fZg7f59+tcB2urbwo2Y1R5Zvlj31wrwk0Iub7A6Npb6HAzWcS5DPHVi+fDm///47Tz/9NPWbt/v3unvCMWpf3kiQ3wQyrG9eZM1dhF2Hl18jatWuX+r+F6S/VwbBiZacTSp53hxTVHOy57Mpw4hJSOb17/76X555gyXU7wW9Xge/7hCxHzbPgNPrckf7+VgaLLivRwt2HAvjUqycPiXMRwK9uE5mtpH95+JKnJY4ODiYGTNm0LVrVyZNun4OvsWZuaRbVeOU380PRwFEhgYRHXGuTEbz1/T3zgAos1E9QIt6njw/pgf/HDjD4o2Hrr9p7QD+w3MXbGv6w5n1sOm/cG4HGP83Jz+ie0sAfpVFWWFGEujFdQ5fSCA1M4cuDUyftklLS+P555/H2dmZmTNnYmHxvx8r94SjeMXsJKjew2RbOhRY/8DmtVjb2tO8Y69S978w3vZGmrtm8fdF826zvNFDAwLo3qoeHyzeTND5AjJdOlSHthOgy3O5C7bHV8DWmXDpKGiNt4cLnZvXZeW2Y+QYTduxI0RxJNCL6+wMiUEp6FTP9BH9zJkzCQ0NZebMmbi7X/8LonnI16RbuXKm9tgC66alJHFy31ZadO6Nte2tbeU0VX+vDA7GWnElvex+7C0sFO9PvIdqTnY8P2c1KemFPC1brQ50mgzt/wPKAg4sgF2fw9UIRvZoyaXYRHYdP1dm/RR3FpN+4pVSA5VSp5VSIUqpqQXc766UOqiUylZKjbzh3gSl1Jm8r4LC/csAACAASURBVAnm6rgoG7tCY2jh7YKLvZVJ5devX88vv/zC448/TpcuXa6753b1BN7R2znlN4Fsy4Lz5RzduZHsrEza9ryn1H0vTn/vDDSKjWU8qndztuejSYMJv5zAuz9uKLygUrnTON1fhhZjICUats+it91JqjnaSqIzYTbFBnqllAGYC9wNNAPuV0o1u6FYOPAwsPiGum7AW8BdQAfgLaWUeR55FGaXkpHNofAEk+fnIyMjefPNN2nZsiVTpky56X7zkK/JsHImuJDRvNaaA5vX4F2/aZktwubX2DmHOg7ZZTpPf02HprWZdG8nft9xglU7jhdd2MIAdTpBz2lQpxPW4du5t3YSmw6cIeaq6U/YClEYU0b0HYAQrXWY1joTWAoMy19Aa31Oa30UuHFScQCwQWsdp7WOBzYAA83Qb1EG9p2NI9uo6dqg+ECfnZ3NSy+9hNFo5OOPP8bK6vq/AKpdDcLnyhZO132QbKuCs0eGBx8n9tIF2pXDaB5yB9D9vTLZdcWapCzzHnRekCeHdSagsQ/v/rCBs5dii69gbQ8tRkOXZxjZzIpso2bVL4sgO6PM+yqqNlMCvTdwId/riLxrpjCprlJqolIqUCkVGB0tBzBUlJ0hMVhbWhBQt/g/uubOncuhQ4d4++238fX1vem+f+g3ZFo6cbrOuELbOLD5T2ztHWnW4ebkZmWlv3cGmUbF1qiynb6B3O2SHz01BGsrS56f84fpaYir1aXekOdp52vHioMx6K0fQfy5Mu2rqNoqxWKs1vobrXWA1jrAw8Ojortzx9oZGku72tWwtSp6r/nevXuZN28e9913H4MGDbq5QNRxal/eyOm648myci6wjZTEBE4F7qRll75Y2ZRsv35ptHXPwt3GyPpymL4BqOXmxHsT7+ZU+BVmLdtqekULS0YP6s35ZEt2X9S5C7VnS3+qlbgzmRLoI4H8QzafvGumKE1dUY5ikjMIupRY7LbK+Ph4Xn75ZerWrctrr71WcKFtH5FlcOBU3QcKbefIjg3kZGeVyyJsfgYF/bwy2HzJ2qw56ovSq00DHhzQjp//PsDmgyEm1xvQvjFuTvYsjm4KNZrl5rw/sgRyssqwt6IqMiXQ7wcaKqX8lFLWwFhgtYntrwf6K6Wq5S3C9s+7JiqZa2mJuxQxP6+1Ztq0acTHxzNr1izs7QvYSXMlCE7+zum648iyKvi8V200cmjrWmo3ao6Hd+lOkboV/b0ySM62YI8Zc9QX58UxPWhapwbTvl3Hlfgkk+rYWFsysmdLNh8+S2TdEdBwQG5mzN1fQFpCGfdYVCXFBnqtdTYwmdwAHQT8orU+oZSarpQaCqCUaq+UigBGAfOUUify6sYB75L7y2I/MD3vmqhkdoXG4GRjSQvvwg/jXrhwIVu2bOGll16iadOmBRfa9jFY2Rd4ROA1Z4MOE3f5Im17FTDtUw4618jE3mAs84en8rO2suTjp4aQkZnNy1+tMflhqDG9WwOwbNNRaHw3tHsEkqJy894nXynLLosqxKQ5eq31Wq11I611fa31jLxrb2qtV+d9v19r7aO1dtBau2ut/fPVXaC1bpD39X3ZfAxRWjtCYrirnjuWhoJ/JIKCgvjoo4/o2bMnDzxQyJRMdDAcXwkd/kOmtWuh7xX4zx/YO7nQtF1Xc3S9xGwN0LNWJn9ftMFYjlPe9bzcee2hPuwNCmf+n/tMquNV3Zne7RqwYuvR3MVcz1bQ+f9yp292fQ5XLxTfiLjjVYrFWFGxwmNTuRCXVuj8fGpqKi+88AKurq689957KFXI1sTtH4OVXW4gKkR8dBTBh/bQtuc9WFqX34j6RgN9MohON7A/xrQHw8zlvu4tuPuuJny+cjuHQy6aVGdc37bEJ6Wxbt+p3AsuvtB5Chiscs+rjTlThj0WVYEEesHW4NwpgO6NCt7xNGPGDM6dO8eHH35ItWqFbL2MDYVjy6H9Y7n5XApx4J8/QEG73oNL3e/S6OOZia1BsyaifHbfXKOU4u1H+lPLzZkX5/5BUmrxe+Q7NqtNPS83lmzIlyjNsQZ0fgZsXWHfPIiRg8VF4STQCzafjqa2mz31qt+cdGzNmjX8+uuvTJw4kY4dOxbeyLaPwWCdO9IsRGZGOoe2/UXTgK44VytZdkxzc7DU9K6VwdoIG3LKeceis4MtHz01mKi4RN5asP5/KY0LoZRiXN+2HA27xNHQfIeX2Lnm/vXk4AH7v4Pzu8u45+J2Zf6z1cRtJT0rh12hMYwO8L1pSiYiIoK3336b1q1b8/TTTxfeSFwYHF0Gdz2RO9IsxLFd/5CemkyHfveaq/ulMsg3g7WRtuyNtqJzjfLdsphpace9vdqx8p9AvDxr0K1toyLLe/t4YWttxeer9vCf+3pcd8/S636anf0Ry59GsKnDt8S6tihxf8bdVbvEdcTtQ0b0d7i9Z+NIzzLSq/H1ATorK4sXXngBoMAUB9fZPit3vrjLM4UW0Vqzb8MqatVpgE+DG1MlVYzetTKwq4Dpm2sGdWtJUz9Pfl6zi4vRRW+XtLO1pnPrBuw9HkZiStp197ItHQmq+yDp1tXotf8JXBOLP6NW3Fkk0N/htpy+grWlxU3nw86ZM4ejR4/yzjvv4O1dRMaL+HO5x+O1exicahVa7FzQYWIuhtOh372FL+aWMztL6OOZwV+RtmRXQOp3CwsLJo7oibWVga+WbyIzq+gUCX06NCM7O4fN+0/ddC/Lypl/7ppPlqUDPQMnYZ9W9Pm04s4igf4Ot/V0NJ3quWNn/b+0B7t37+bbb79lxIgR3HNPMU+ubp8FygBdni2y2N71v2Hv5IJ/hx5Flitvg33Tic2wYE90+e6+uaaaswOPD+/Bhag4lm/YX2RZ7xrVaNnQl417TxT4SyHVzostAV9hmZNOz8BJWGXJcYQilwT6O9j52BTCYlLo2fh/u23i4uJ45ZVX8PPzY9q0aUU3EH8eDi+GdhPA2bPQYtGR5zlzZC8BfYZW6JbKgvSslYmDpZE1EeWXb+dGrRvXpl9HfzbsOcHh0+FFlr27SwuSUtLZdaTgVApXnRqwre2nOKWcp/vBZ7HIKeTgE3FHkUB/B9tyOjdT6LX5eaPRyLRp00hISCg8xUF+Oz7JPR2pmNH87r9WYGltQ/s+Q8zSb3OyNUA/r0zWRdqQVYEn943q1x7fWm7M/20b8YmF56Bv4udJHU93/tp1DGMhT3tdce/Anpb/pWbcfjoee0MSoQkJ9HeyzaevUNfdnrp52yoXLFjA1q1befnll2nSpEnRlRMuwKFF0PYhcCl8Dj8xPoZjuzbRptsA7J0KT69QkQb5pJOQacGOyxX314a1lSWTRvUmIyubb1ZuwVhIigSlFHd3bUlUzFWOBBc++j/vNYjDjZ6h7qW1NAv7rqy6LW4TEujvUOlZOewOjaVn3mh+//79fPrppwwcOJDx48cX38COT3L/LWY0v+/vVWijkbsGjihtl8tM95qZuFob+S284qZvALw8XHlwUGeCzl7it80HCy3Xvpkf7i6OrNt5rMj2TtZ7jLNeg2gV/AXel7eYubfidiKB/g61OyyWjGwjPRt7EBMTwwsvvICPjw/vvvtu8btirkbAwZ+hzQPgevOhI9ekp6ZwYPMamnXoTjWPwnfkVDQbAwz1TWd9pA2J5XDyVFG6tW1Et7aN+GPrYY4GF5zHxmCwoH+n5gSfjyL0QhGJzZRiX/O3iXNuSucjU3FODiujXovKTgL9HWrzqSvYWlnQvo4rL730EomJiXz22Wc4OhZ87N91dszO/bfb80UWO7hlDZnpqXS6e2SR5SqDEXXSyTAq1lyomD31+T04qDO+Nd2Yt3ILMQkFpzTu3q4R9rbW/Ln9cJFt5Rhs2db2M7INtnQ/MAWrrKsARMSnsuboReZsOsN7a4NoM/1vhn+5k3f/PMnpKNPSKIvbhwT6O5DRqPn7xGW6N/Rg/jdfs2fPHt544w0aN25cfOX483DgR2gzHlwLf5oyKzODvet/w8+/DZ51G5qx92WjZbVsGjhls+J8xU7fQO58/dNj+2A0Gvly2Saysm8+IcXOxpoBnZpz6FQ454s5jzbNrhbb287GIS2S9oEv8sP2EL7cEsres3HYWhlo6unE3S08sTJY8POe8wz4dBuPfL+P8NjUsvqIopxJoL8DHY28SlRiOvVyLvD1118zfPhwRowwcQ59y8zcnTbdXy6y2MHNa0i+Gke3IYWfGVuZKAUj66ZzINaas0lFH6VYHmq5u/DY8O6ERUazdP3eAsv07eiPna01q7cUPp9/TbRra5Z6PEPdhD2MSVrAQP9aTLunKY93q8fwNj68N7wFvzzRiT2v9uHlgY3Zfy6efrO3snhv0ds9xe1BAv0daP2JKAypsfz69UwaNmzIG2+8YVrFK6fg6FLo8J8id9qkpaWxc80v1G3aijpNWpqp12VveO10LND8WglG9QABzfwY0Lk5/+w9ye6jN++bd7CzoX9Hfw4EnedCVOGj+myjkV8PRvJaeDtW2wziMfUHDzruL/BsYDcHa57q2YCNz/fgrnruTPvtGK+vOkZOeSbuF2Yngf4OtO7QOZwP/oSFUsyZMwc7OzvTKm56F6wcoGvRc/NLly4lJTGeHvc+aIbelp+adka61szk13Dbcj2QpCij+nWgcZ1aLFi1nXMXY266379Tc+xsrPh9y6ECakN2jpFFe8I5EB5P7yY1SO4xnSvV2nLXsbeKzIlTy8WW7x9uzxPd67FwTzjPLTtMdk4FPmggSkUC/R0mOOoqFzfMJyP+ErNnz8bXt/BdM9eJOACn/sxLi1v4AeKpqal89913+Pm3oXbjkmdRrGgj66YTmWqosJQIN7I0WPD0mD44O9jx+eINJCRdP2/uYGdD347+BJ48x+ULZ6+7l200smRfOKcvJ3Fva2/6Nq0JBmt2tJlFppUz3Q4+++/ibEEMFopX72nK1LubsPrIRZ775UihD2mJyk0C/R1m+oefYbh0nKenPE+nTp1Mr/jPO2DvDp2eKrLYkiVLiIuLu+1G89f098rAycrI8nMm/pVTDpwd7Zgyrh/JaRnMWbrxpsXZAZ2aY2tjxbbfF/57TWvNqkMXCYpKYmgrLzr4uf17L92mOjvazMI+PYouR6ai9M2Lvfk92aM+rwxswh9HLvLe2iDzfjhRLiTQ30E2btzIgXVLqNasC09NfNT0iqGb4OxW6PYC2DgVWiwlJYX58+fTpUsXfBv6F1quMrM1wDDfdNZE2BCfUTmybALU8XTn8eHdCblwhZ//3HndYSWO9rYM6NScU4E7iAzNzWy5+XQ0B/Oma27MTAoQU601B5q9ilf0Dpqf+arY93+yRz0e7lyX73ac5efd58z1sUQ5kUB/hwgODuall1/B6OrLE8++Ynqq4JxsWP8auNaBgMeKLPrtt98SHx/PlCmFnzJ1O3igfhqZRlUptlrm16F5PYZ0b822g8Fs3HvyunsDu7TAwbkaG5Z9w4nIq2wMukxrX1f6NCn8IJgQ31GE+gynReg8OLWmyPdWSvHG4Gb0blKD6X+e5GB4vFk+kygfJgV6pdRApdRppVSIUmpqAfdtlFLL8u7vVUrVzbteVymVppQ6nPf1tXm7L0wRFRXFxIkTsbC2I7vjwwxpW8f0ygd/hCsnof+7YFV44Lt06RI//PADgwYNomXL22enTUGauOQQ4J7JojC7SrMoe83w3u1o06Q2i9ftuS7TpZ2NNT3ufYALwSdY8edfeLvaMbyNd9G/0JVif7PXiHXxh1+fKPaQcYOFYvbo1tRyseXpRQeJTS7+vFtRORQb6JVSBmAucDfQDLhfKXXjEUGPAfFa6wbAbOCDfPdCtdat876eNFO/hYmSkpJ44oknSE5OxrrnE3RuXh83BxOTd6UlwOYZUKcrNB1aZNHZs2ejtea5554zQ68r3gP10ziXbFmhic4KYmGheGJEL2rXcuPLXzYRFhn9773mXQdg4VwTi+N/MjbACytD8eM4o8GG7W1mg6U1LB0PGUU/Fetib8VX49sRl5LJlKWHZNvlbcKUEX0HIERrHaa1zgSWAsNuKDMM+DHv+xVAH1VZjhG6g2VmZvLMM88QFhbGpFf/yyXcuK9tEadF3WjbR5AaBwPfy32iqBDHjx/njz/+YMKECUWfRnUbuds7g+o2OXwfUnkWZa+xtbHiuQcG4Oxgy+yF67kcm7tz5q+TV0hrcjckXeHc/k0mt5dq5wmjfoDYM7DqqWLTGjf3duHde5uzMySW2RuCS/NRRDkxJdB7A/mzK0XkXSuwjNY6G7gKXFsB8lNKHVJKbVVKdStlf4WJtNa89dZb7N69m+nTp3PK6ImjjSUD/E1MLhYTAnu/zk1c5tmqyPeZOXMmbm5uTJw40Uy9r3g2Bniofhqbo2wISaz4J2Vv5OpkzwsPDURrzSc/r2dLpIG9Z+Po3LUHtRs1Z+uqn0lPSTa9Qb/u0G86BK2GnZ8WW3x0gC9jAnyZuyWEXSE37+8XlUtZL8ZeAmprrdsAzwOLlVLONxZSSk1USgUqpQKjo6NvakSU3BdffMGqVauYPHky/e8ZwppjlxjUwhN7a8viK2sN66eBpR30Lvqp2b///psDBw7wf//3f6YlRLuNjK+fhrWFZkFIMQewVBDP6q48O64/sYkp/PDLWrydDPRvXov+454kJekqW379sfhG8us0Gfzvg3+m5+60KsZbQ5vhV92B5345THyKnGRVmZkS6COB/E/V+ORdK7CMUsoScAFitdYZWutYAK31ASAUaHTjG2itv9FaB2itAzw8PG68LUro+++/56uvvuK+++7jqaee4q/jUaRm5jAywMe0Bk6ugjProecr4FSz0GLJycm89957NG3alJEjK3+GypJyt9GMqJPOynO2xKRXzplIP9+auHQaDfEROB5cCDnZeNZtSEDvwQRu+pNL54peYL2OUjBsDng0gRWP5iawK4K9tSWfj21DXEomr6w8et2WT1G5mBLo9wMNlVJ+SilrYCyw+oYyq4EJed+PBDZprbVSyiNvMRelVD2gISBJscvQsmXL+PDDDxk4cCDTp09HKcWSfeHUdbcnoE614htIi4e1L4Nna7hrUpFFP//8c6Kjo3n77bextDThL4Xb0OONUsk0wvwzlXNUv/JSdSLc2tGtTx/CTx7g169nkpOdTa/7HsbeyZl1P81BF3JaVYGsHWDMQjAaYdkDkJVWZPHm3i68MrAJf5+8zJJ9BefPFxWv2ECfN+c+GVgPBAG/aK1PKKWmK6WubcWYD7grpULInaK5tgWzO3BUKXWY3EXaJ7XWceb+ECLX6tWreeedd+jRowcffPABBoOBkxcTCTwfzwMd65i2d37Dm5AaC0M/B0Phwfv48eMsWrSIsWPH3vbbKYtS3ymHQT4Z/BRqR0Jm5RrVn0yy49dL7vRwT+CxHnUZMH4Spw/s5PfvPsLazo6+Y/5DZNgp9v/zR8kadq8PI76FqGPwxzPFLs4+2sWPbg2rM/3PE4RckVz2lZFJc/Ra67Va60Za6/pa6xl5197UWq/O+z5daz1Ka91Aa91Bax2Wd32l1to/b2tlW611CX/ihKlWrVrFq6++SocOHfj000+xts7dFrhw73lsLC0Y2c6EaZtzO+DgT9Dp6SIXYDMzM5k2bRru7u5VZjtlUSY3TSEl24LvK9GoPjnbgjlnvahpk8UjvrmnTHXody+9Rz3KiT1b+GP+J/h37EmDlu3ZtHw+cVculuwNGg2A3q/B0WW5u6+KYGGhmDWqFfbWlvzfksNkFJA/X1QseTK2ClixYgXTpk2jQ4cOfPnll9ja5j7YlJiexapDkQxt5YWrfTH7wbPSc0dvrnWg56tFFp0zZw5nzpzh3Xffxcmp8JQIVUUTlxwGeKWz4IxdpUiLoDV8c74WCdmWTPG7iJ3hf1MzXQaNocfwhzi6cyOr5n3IwAeeRlkY+HPB7JJN4QB0exFa3Z/7LMWxFUUWreFsy0cjWxJ0KZEP/yo8K6aoGBLob3NLlizhjTfeoGvXrnz11VfY2/9v1Lls3wVSM3N4sJMJT8JufAtiQ2DIp2Bd+Mj18OHDzJ8/nxEjRtCjRw9zfITbwovNU0jJVsw95VDRXWFTjAt7E5wZ6xVNfYf0m+53HzaePqMf5+S+rfy9ZB59Rj/K+VNH2bthVcneSCkY8hnU6ZK7vz684ANQrunTtCYTOtVh/o6zbDldxFm2otxJoL9Naa358ssvmT59Or169WLOnDn/juQBMrONzN9xlo713Gjp41p0Y6fX5e6Zv2sS1O9daLHExEReeuklatasydSpN2XCqNIaOucwom46P4XaEZlacf9tItKs+eFCTVo4pTC4ZuHLXZ3vGcXAB54i+NBuTgXupEHL9vzzy3wunb/5AJMiWdrkLs66+MDS+yE2tMjir97TlMY1nXhx+RGikyRFQmUhgf42lJOTwzvvvMMXX3zB8OHD+eyzz/6dk79m1eFIohLTebJH/aIbS7yUO1qr1QL6vVNoMa01b7zxBlFRUcyaNavK7Zk3xXPNUlDA+0cr5rNnGhWfn/XCxmDkab+LWBQzi9S+7zCGPvYC504d4WpsNPaOzvz61ftkphe9k+Ym9m4wfnnu9z/dC4mFz/fbWhn4/P42JKZn89KKI7LlspKQQH+bSUlJ4ZlnnmHZsmVMnDiRGTNmYGV1/SEZOUbNvK2hNPV0pkejIp5LMObAr/+B7HQYsSB39FaIxYsX8/fff/Pss8/Spk0bc32c24qXvZGnmqTwZ4Qtu66U78EkWsO352txPs2Wp+peopqVaQuerbr1Z+yz00mIiUJrTdzlSP78/tOSB2D3+vDAytzttz8Pz02NUYjGtZx47Z6mbDkdzQ+7zpXsfUSZkEB/G4mMjGT8+PFs3ryZ1157jeeee67ALZO/H44kNDqFp3vVL3pL5Y5P4Nx2uPtD8LjpObZ/7du3j5kzZ9KjRw8eeeQRc3yU29YTjVOp7ZDDG4ecyCzHk/X+iq7GtjgXRnpG09YlpUR1G7Rsz4RXPwbAYLDkxN4t7Pmr6MXVAnm1gfuXQNxZWDQSMgpPsfBQpzr0blKD99edIuhSYsnfS5iVBPrbRGBgIKNGjeLixYvMmzePBx54oMBymdlGZm8Mxt/LmXuaexbeYPDfsGkGNB+Zm8+mEBERETzzzDPUrl2bjz76CAuLO/tHxtYA77ROIjTJks9Ols/C7MkkO366UIMAlyRGeBZ+CHhRPOs25NE3P8PdM/ch943L5hNydH/JG/LrBqO+h4uHYcnYQoO9UoqPRrbExc6KKUsOkZ4lWy4r0p39v/Y2YDQaWbBgAY888giurq4sW7aMrl27Flp+2f5wLsSl8eKAxlgUNokbHQwrH4NazXMfjCpk1H/16lUmTZqE1pq5c+feEVspTdHLM5PRddP46pQ9B2PL9ongmExLZod5U8smk6f9LhU7L18U1+o1efT12TRp1xXQLPv0Lc6fPlbyhpoMguHz4PxOWDgC0gsesbs72jBrVCvOXEnm3T9PFlhGlA8J9JVYfHw8Tz31FB999BG9evVi6dKl+Pn5FVo+ITWTTzYEc5efGz0Lm5tPugyLRuTOx49dkvvIewHS0tKYNGkS58+f59NPP6Vu3bpm+ERVxxutkvG0N/LsPheultETs8nZFrx/xpcso+LFBpHYG0o/V2RlY8vIya/TZfD9GI05/DzzZU4d2FnyhlqOgpELIDIQfr43d+6+AN0beTCxez0W7Q1nyb7wAsuIsieBvpLauXMnw4cPZ9euXbz++ut89tlnODvflPjzOh+tP01iejbvDPMveG4+PTF3bjUlBsYtA1ffm8vwvzz2R44c4eOPP6Zjx47m+EhVipOV5vO7rnIp1YJn9jmTY+bNJek5ig9CfIjKsOKlBpF425ovO6RSit4jH+beJ14BNMu/mM4nn3xCTk4Jp1f8h8Pon3NTJfw4FJIL3jv/8oDGdG/kwRurjrMrVFIaVwQJ9JVMcnIyb775Jo8//jiOjo4sWbKE8ePHF5un5vCFBBbvC+ehTnVoUquAXwgZybBoVO6xgKN+BO92BbaTnp7O5MmT2b59O2+99Rb9+/c3x8eqktq5Z/NW6yS2RNkw44hjcSlhTJaWY8H7Ib6cSbFjit8l/J1SzdPwDVp06s34F9/HwmDg22+/ZeTIkYSElHCffZN7cv8yjDkD3/aByzdP0VgaLJgzrg1+1R2YtPAgYdElyJMvzEICfSWhteaff/5h6NChrFy5kscee4yVK1fi7+9fbN20zByeX3aYWs62PNevgN0zGUmweAxE7IMR30GjgoN3SkoKkyZNYseOHbz77ruMHj26tB+ryhtfL52HG6SyIMSez4JKnwsnMcvAjDO+BCfbMcXvIndVK9skYX7+bZgw7RNsbW0JDg5m+PDhfPXVV2RmluAviIZ94ZG1kJMJ8/tDyMabijjbWjF/QnsMForHfgyU/PXlTAJ9JXD+/HmeeOIJJk+ejKOjIwsXLuTFF1/Exqbwfe35zVwXRFhMCh+PaoWz7Q37u1Pj4KdhEL4bhn+T++d2AS5dusT48ePZv38/M2fOrJL55cuCUvBmq2RG1knj05OOzDjieMsHioen2fDaqTqcS7XhuXqRdHYrn0yQPvWbsHDhQlxcXFBK8fnnnzNkyBA2b95seiPebeE//0C1urBoNOz56qasl7Xd7Zn3YDsiE9J4+Pt9JKVnmfeDiEJJoK9AcXFxvP/++wwZMoSDBw8ydepUVq5cWaIHkv44cpEfd5/n0S5+dGlQ/fqbsaG5I6yo47mPsbccVWAbhw8fZsyYMURGRjJv3jyGDi36IHBxPQsFHwQkMaF+Kt+esec/u1yILsFBJUYN665UY1pQHTKMFrzdOJwO1cp3esPf35+lS5fi6emJpaUlqampPPXUU0ycOJGgoCDTGnHxgUfX5Wa+/GsqLB1304NV7eu68eW40LBMLQAAEIpJREFUtpy4mMhjPwSSnJFdBp9G3EgCfQVITExk7ty59OvXj4ULFzJkyBDWrl3LhAkTbnrKtSgnLl7lpRVHCKhTjal3N7n+Zuhm+K5Pbm75h1blzqXeQGvNDz/8wIMPPoiNjQ2LFi2iS5cupf14dySDgrdbJ/N26yS2X7am/9/u/Bxqx/+3d+5BUV15Hv/8aMSQBnmI7wYUMSg+QQ3qpIwzBB+R0sTZMkZT60ST2cxOdjLJTqbiTtWsa21NHuMmNUmcmTiZlDEvnE2iskk0mESRlAZFBCO+EPDBGxR5CvI4+8e9aIMNtErTHT2fqlt9+t5z7/32uff8+t7fOed3Grtp32xTkFVtZc3xkWw6P4QJ/g38MbqASAeByvqCsLAwkpKSmD59OpWVlUyaNImsrCyWLFnCs88+S0FBQc8H6e8Pyz6EeS9C7i74y4+gIK1Dlgeih/CnZTEcOlfFY2+nU92gn+xdjXhaLIpp06apjIwMd8twCeXl5WzevJmkpCTq6+tJSEjgmWeeYfToHuLROOBMZT1L39qPlwjJ//YjBvubAc1aW2DvK5D6CgyKMkYyBkdct39xcTFr164lLS2N+Ph4/vCHP/TYq+dG+DD95rvSjT73v72mo524UcG9fsyuyK2xsOaQPxkXfAjp38rcEVeIC7mC7W7D6lc0Wfg8v4UDl/wpa/JhkE8zj44oZ1ZQbVdDGpwiL8zxG5szLI8Lu5pubW3l9ddfZ+PGjYSFhREbG0tKSgqNjY0kJCSwatUq5yabKc4ypiS8mA/THof434PvtVnOUnJKefrDw4QPvJt3fjad0GDPiff/Q0REDimlpjncpg29a1FKkZWVxUcffcTOnTtpbW1l3rx5PPHEE0RHR9/UMc9fbGDZxu9ouNLCln+ZyT1DzIFMFSdh2y+g6BBMXg4L11/XT76lpYUtW7bw2muvoZTiueeeY/ny5c7NPnUD3MmGHgz39P6KfmzO8yWtzIf6lo4vz97Sxli/y/w4pJq4wFr6ed16PewtQ99Oeno6a9asoaysjCVLlmC1Wvn000+pra1l6tSpPProoyQkJFwXUK8DTXXwzX/DgbfANxgS1sGU5VcH6e3Lq+QX72fi7SVsWBHLjIiBN/0b7nS0oXcDFRUVfPHFF2zbto0TJ05gtVpZtGgRK1euJDzcifjwXfB9YTWPbzrIlZZWPnxyBhNGBBiVKW097HvTeHVeuB4m/LTDfkopUlNTWb9+PXl5ecycOZN169Zhszk5YfgNcqcbenuaWqGgzkJJgwURCPZpo7qqAp9eMO729LahB6O776uvvsqWLVsIDAxk1apVKKVISkqiqKiIoKAgHn74YRYuXMi4ceO6fmAoOQKf/7vR82t4DNz/guHLFyGvoo4n383gzIV6nku4h6fuH423RXuVbxRt6PuIsrIyUlNTSUlJYf/+/bS1tREdHc3SpUtJTEzEar352ChKKf6RcZ61yccItvqw6fHpjAkEDvwN9r9p+OKnrIAH/gv8ro2KbW1tZdeuXWzcuJHjx48TFhbG888/T3x8fK8/xdujDX33pBf0/tTJrjD07Rw7dowXX3yRjIwMBg8ezOrVq7HZbGzdupXdu3fT2tpKWFgYCxYsYP78+URFRV1/f7W1wZEk2PMSXDprTFc5+7cQtYC6ZsV/fPo9ydnFTLIF8NKSSUQP7z1X4p2ANvQuorm5mZycHPbu3cuePXuu9k6w2WwsXLiQxMREIiMjb/k8hVUNrPu/Y6QcK2NmxEDeWDiEkNwtRhe2xksQ+YAx/Z/t2jUuKytj+/btfPLJJ5w7d46RI0fy5JNPkpiY2P2rdi+hDX33/NAMPRgPGwcOHGDDhg0cPHiQAQMGsGjRIubNm0d+fj47d+4kPT2dtrY2bDYbs2bNYtasWcTFxREYaDf5TWuzORfteqgqgIBQiHkMNWU5n5/z5j+351DVcIVHpofxq/hIhgX43vTvupPQhr6XqK6u5ujRoxw6dIjMzEyys7NpbGzEy8uLmJgY7r//fubMmUNkZGSvPC2X1zTy9rcFbN5/hrtp5JUJhcQ3fYMU7AHVBvcsgNnPg80Y5VpSUkJqaipff/01+/bto62tjalTp7JixQrmzp2LxWK5ZU3Oog199/wQDb09GRkZJCUlkZKSQnNzM+PHjyc+Pp6pU6eSn59PWloa6enp1NfXIyKMHz+emJgYJk6cyMSJEwkPD0faWuHEZ5D5rtFLDGDkfVyOmMvG8rG8kdmCCPw01sZjM8INN6WmS7Shv0Gqq6s5f/48Z8+eJTc3lxMnTnDy5ElKS0sB8PLyYty4ccTGxhIbG0tcXBxBQUE9HNU5ahqb+Ta3kh2ZBZTmHmAGR1nsf4rRTceQtmYICIPJy2DyMspa/MjMzOTw4cMcOHCAkyeNSZltNhuJiYk89NBDt9QecCtoQ989P3RD305VVRXJycns2LGD7OxsAIYPH869995LTEwMVquVgoIC0tPTycnJ4fJlY3arAQMGEB0dTWRkJBEREYwbdjdRDQe5q+ArpMJ4M24OGsNhr2g+Lh/Bdy1j8B00mp9ED+EnYwcTExqo/fiduGVDLyLzgT8BFuBtpdRLnbb3BzYDU4ELwCNKqTPmtjXAaqAV+JVS6svuzuVKQ6+UoqamhgsXLlBZWXl1KS8vp6ioiHPnzlFYWEhNzbWwq97e3owaNYqoqCiioqKIjo5m8uTJt+RvN8XAlXr2Hc2lsiifyxUFNFWeIaAun7FyltFexXjTRmMLlFrHUzpgEgXKRl6V4nReHnl5eVRWGgGi7rrrLiZNmsTs2bOZM2cOERERLvW/O4M29N1zuxh6eyoqKti9ezdpaWkcOnSIqiojoqWvry+RkZFERkYSHBxMU1MT5eXlFBYWcubMGRoarsXysVqtxIQH8kBYM1MDqgiTMnyUMa6gHl9OtgzjFKEUWUIh0IY1JJSgoaPwCx6K1eqHv68P/b29uNLaxiC//ndUl83uDH2PwbRFxAJsABKAQuCgiCQrpeyjF60GqpRSkSKyDHgZeEREooFlwHhgOPCViNyjlOr1WQjq6urYtGkTtbW11NXVUVtb2yFdV1dHTU0Nzc3XD87o168fw4cPJzQ0lMmTJxMaGorNZiMsLIxRo0b1rk/7q7Vw+AMjrGtbM97lPlRe7Ef1FS+qr3hR2eLLx8qP2taxlNVc4VJtA1AFpAJGRRg9ejSzZ88mKiqKmJgYxo4de0MDrTQaVzBo0CCWLl3K0qVLUUpRUFBAZmYmp06dIjc3l9TUVC5e7PgH5+fnR3h4+NU6ppTifH0zf85sprbWm8bLQQzxbSUyoIVwvxZG+pcSOaCQuLu/xVIPlmLw/l5h8TIGoF1WPjQpb3zEC+nfj2pfHxAvxMuLkxGrqQuZgo+PD/369bvu02Kx4OXl5dRisVgQkavf3f1g1RPOzJpwL3BaKZUPICJJwGLA3tAvBtaa6Y+BN8X45YuBJKVUE1AgIqfN4+3vHfnXaGlpYcOGDVitVvz9/a9+BgUFERoair+/P/7+/oSEhFxdBg4cSEhICAEBAX03c9LAMcYoVd8g8A1i2/v72ZqdjbfFQkBAAAGBgQQEBDA8MJApgwczbNgwhg4dytChQwkPD2fIkCEef1NpNCJCREQEEREdB+tduHCBwsJCiouLKSkpobi4mIqKCi5dutRhufZAJpRe9qb0sjff3qCG1VG1jA+ux0uMMBVvbX+TnCrXdkRor5s9fdrnt982YcIE3nvvvV7X5YyhHwGct/teCMR1lUcp1SIi1cBAc/13nfYd0fkEIvJz4Ofm1zoROdkpSwjgqYGstbYbx1N1wQ9a229u+sArbnpPwEPL7PkTQAdtjuPlu5Hryi0rK4v333//Zo/XZYOca+dBcxKl1EZgY1fbRSSjK9+Tu9HabhxP1QVa283gqbpAa2vHGX9FEWA/FZHNXOcwj4h4AwEYjbLO7KvRaDQaF+KMoT8IjBGRUSLig9G4mtwpTzKw0kz/E/CNMrrzJAPLRKS/iIwCxgAHeke6RqPRaJyhR9eN6XN/GvgSo3vlO0qpHBFZB2QopZKBvwPvmY2tFzH+DDDz/QOj4bYF+OVN9rjp0q3jAWhtN46n6gKt7WbwVF2gtQEeOGBKo9FoNL2LHlqm0Wg0tzna0Gs0Gs1tjkcaehFZKyJFIpJlLtfPg2fkmy8iJ0XktIi80Efa/igiJ0TkiIhsFZHALvKdEZHvTf0uDd7TUzmYjeFbzO3pIjLSlXrMc4aKyG4ROSYiOSLyjIM8c0Sk2u46/97VuuzO3e31EYPXzTI7IiKxfaQryq48skSkRkR+3SlPn5WbiLwjIuUictRuXbCI7BKRXPPTYaAnEVlp5skVkZWO8vSyLo+om11oc69NU0p53IIxyvY3PeSxAHlABOADZAPRfaBtLuBtpl8GXu4i3xkgpA/09FgOwL8CfzXTy4AtfaBrGBBrpv2BUw50zQE+c9M91u31AR4EdgACzADS3aDRApQC4e4qN2A2EAsctVv3CvCCmX7BUR0AgoF88zPITAe5WJdH1M0utLnVpnnkE72TXA3NoJS6ArSHZnApSqkUpVT71PXfYYwNcCfOlMNi4F0z/TEQL53HYvcySqkSpVSmma4FjuNgVLQHsxjYrAy+AwJFZFgfa4gH8pRSZ/v4vFdRSu3F6Elnj/399C7wkINd5wG7lFIXlVJVwC5gvit1eUrd7KLMnMFlNs2TDf3T5ivYO128GjoKzdDXhmQVxlOfIxSQIiKHzBAPrsKZcugQogJoD1HRJ5iuohgg3cHmmSKSLSI7RGR8X2mi5+vjCffXMuCjLra5q9wAhiilSsx0KTDEQR53l58n1M3OuM2muc3Qi8hXInLUwbIY+AswGpgClAD/40Ha2vP8DmNswAddHOY+pVQssAD4pYjM7gPpHoeI+AGfAL9WStV02pyJ4ZaYDLwBbOtDaR59fcQYnLgIcBSz2Z3l1gFl+Bw8qo+2h9ZNt9o0t8W6UUo94Ew+Efkb8JmDTS4Lr9CTNhH5GZAIxJs3uqNjFJmf5SKyFeO1bG9v6OvEjYSoKJSOISpcioj0wzDyHyilPu283d7wK6W+EJE/i0iIUsrlAbKcuD7uDt+xAMhUSpV13uDOcjMpE5FhSqkS053lKFpYEUZbQjs2YI+rhXlY3bQ/59Xr6A6b5pGum06+0IeBow6yOROawRXa5gO/BRYppRq6yGMVEf/2NEYjkaPf0BvcSogKl2G2AfwdOK6UerWLPEPb2wpE5F6M+7Ev/oCcuT7JwD+LwQyg2s5d0Rc8ShduG3eVmx3299NKYLuDPF8Cc0UkyHRTzDXXuQwPrJv253WvTXNVy/Mttlq/B3wPHDF/6DBz/XDgC7t8D2L05sgDftdH2k5j+NGyzOWvnbVhtJpnm0uOq7U5KgdgHcYND3AXhgvgNEasoYg+KKf7MF7pj9iV1YPAU8BTZp6nzfLJxmg8m9VH19Dh9emkTTAm3Mkz78VpfaHNPLcVw3AH2K1zS7lh/NmUAM0YPuPVGO07XwO5wFdAsJl3GsYMdO37rjLvudPA432gyyPqZhfa3GrTdAgEjUajuc3xSNeNRqPRaHoPbeg1Go3mNkcbeo1Go7nN0YZeo9FobnO0oddoNJrbHG3oNRqN5jZHG3qNRqO5zfl/e2373KoyfrYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WPOsofeOXspH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 90
        },
        "outputId": "46f2ede8-7f44-4755-b468-38355298ba50"
      },
      "source": [
        "# ex) 영업사원과 감사부사원의 하루 출장비에\n",
        "# 차이가 있는지 검정하시오 (유의수준 0.10)\n",
        "# sales : 131 135 146 165 136 142\n",
        "# audits : 130 102 129 143 149 120 139  \n",
        "# 영업부서가 감사부서보다 출장비가 많다고 할 수 있는가?\n",
        "\n",
        "sales = [131,135,146,165,136,142]\n",
        "audits = [130, 102, 129, 143, 149, 120, 139]  \n",
        "\n",
        "# 귀무가설 : 영업부서가 감사부서보다 출장비가 같거나 작다 (<=)\n",
        "# 대립가설 : 영업부서가 감사부서보다 출장비가 많다 (>)\n",
        "\n",
        "# 정규성/등분산성\n",
        "print(stats.shapiro(sales))\n",
        "print(stats.shapiro(audits))\n",
        "print(stats.bartlett(sales,audits))\n",
        "\n",
        "# 독립표본 t검정\n",
        "stats.ttest_ind(sales, audits)\n",
        "\n",
        "# => ttest_ind 함수의 결과는 양측검정을 위한 값임\n",
        "# => 따라서, 단측검정one-sided을 하려면, p-value/2로 비교함\n",
        "# => 0.153 / 2 => 0.0765~\n",
        "# => 유의 확률 0.10기준 pvalue가 작으므로 귀무가설 기각 \n",
        "# => 영업부 출장비가 많을 확률이 높음"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(0.8661074638366699, 0.21112492680549622)\n",
            "(0.9487473964691162, 0.7182835936546326)\n",
            "BartlettResult(statistic=0.3146541578335654, pvalue=0.5748381522579644)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_indResult(statistic=1.5367956504902474, pvalue=0.1525942542150006)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wWUhGxKFct9n",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "59cba4eb-47bb-41cc-a51b-0e48ebf2590e"
      },
      "source": [
        "# ex) 모델회사의 두 모델 수입이 다음과 같을때\n",
        "# kim이라는 모델이 park 이라는 모델의 수입보다\n",
        "# 크다고 할수 있는지 유의수준 0.05로 검정하시오\n",
        "# kim : 5, 4.5, 3.4, 3.4, 6, 3.3, 4.5, 4.6, 3.5, 5.2, 4.8, 4.4, 4.6, 3.6, 5.0 \n",
        "# park : 3.1, 3.7, 3.6, 4.0, 3.8, 3.8, 5.9, 4.9, 3.6, 3.6, 2.3, 4.0\n",
        "\n",
        "kim = [5, 4.5, 3.4, 3.4, 6, 3.3, 4.5, 4.6, 3.5, 5.2, 4.8, 4.4, 4.6, 3.6, 5.0]\n",
        "park= [3.1, 3.7, 3.6, 4.0, 3.8, 3.8, 5.9, 4.9, 3.6, 3.6, 2.3, 4.0]\n",
        "\n",
        "t, p = stats.ttest_ind(kim, park)\n",
        "print(p, p/2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.11421599270766702 0.05710799635383351\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VgL1wMOaiLu7",
        "colab_type": "text"
      },
      "source": [
        "# 짝paired 표본을 이용한 가설검정\n",
        "* 동일한 집단의 전/후 차이를 비교하기 위해 사용\n",
        "* 짝paired 표본 : 동일한 모집단으로 부터\n",
        "  추출된 서로 연관있는 2개의 표본을 의미\n",
        "* 주의점 : 짝paired 표본의 갯수는 서로 동일해야 함\n",
        "* 파이썬에서는 ttets_rel함수를 사용해서 짝표본 t검정 시행"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tCMYSqJvjAda",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 90
        },
        "outputId": "5b42158c-7755-4cb5-f435-302fb35c5787"
      },
      "source": [
        "# ex) 10명 학생의 과외 받기 전/후 수학 \n",
        "# 성적차이를 비교하시오 (유의수준 0.05)\n",
        "\n",
        "before = [16,20,21,22,23,22,27,25,27,28]\n",
        "after = [19,22,24,24,25,25,26,26,28,32]\n",
        "\n",
        "# 정규성, 등분산성 확인\n",
        "print(stats.shapiro(before))\n",
        "print(stats.shapiro(after))\n",
        "print(stats.bartlett(before, after))\n",
        "# 짝 표본 t검정\n",
        "print(stats.ttest_rel(before, after))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(0.9480883479118347, 0.645940363407135)\n",
            "(0.9554644823074341, 0.7331799864768982)\n",
            "BartlettResult(statistic=0.051569421877824824, pvalue=0.8203545237328987)\n",
            "Ttest_relResult(statistic=-4.47213595499958, pvalue=0.00154988591170182)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rgc8XvVTkImB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "08951879-475a-4fed-debc-011a3ef755d4"
      },
      "source": [
        "# ex) 상호금융회사는 부동산 가치 평가를 위해 2개의 평가회사를 고용했음\n",
        "# 임의로 10채의 주택을 추출해서 각 회사에 주택 가치평가 의뢰 \n",
        "# 평가 회사별 가치 평가 차이가 있는가? 유의수준 0.05로 검정하시오  \n",
        "\n",
        "# woori : 235, 210, 231, 242, 205, 230, 231, 210, 225, 249\n",
        "# shinhan : 228, 205, 219, 240, 198, 223, 227, 215, 222, 245  \n",
        "\n",
        "woori = [235, 210, 231, 242, 205, 230, 231, 210, 225, 249]\n",
        "shinhan = [228, 205, 219, 240, 198, 223, 227, 215, 222, 245]\n",
        "\n",
        "print(stats.ttest_rel(woori, shinhan))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ttest_relResult(statistic=3.304500684012972, pvalue=0.009163900170900421)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RTVHsgn4kZoN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "685f4d52-4b80-484d-ace1-72c083339726"
      },
      "source": [
        "before = [320, 290, 421, 510, 210, 402, 625, 560, 360, 431, 506, 505]\n",
        "after = [340, 285, 475, 510, 210, 500, 631,560, 365, 431, 525, 619]\n",
        "\n",
        "t, p = stats.ttest_rel(before, after)\n",
        "print(p/2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.02500246921848288\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}