Copy_of_LS_DS_123_Confidence_Intervals_Assignment.ipynb

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        "<a href=\"https://colab.research.google.com/github/thecodinguru/DS-Unit-1-Sprint-2-Statistics/blob/master/Copy_of_LS_DS_123_Confidence_Intervals_Assignment.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "## Confidence Intervals\n",
        "\n",
        "The following url can be used to access an abbreviated version of responses to Stack Overflow's 2018 Developer Survey. The original Survey had ~100k respondents but the data is quite dirty so I have selected a cleaner subset of it for you to use for your assignment.\n",
        "\n",
        "<https://raw.githubusercontent.com/ryanleeallred/datasets/master/bootcampers.csv>\n",
        "\n",
        "The provided dataset holds 14 columns of information about individuals who make less than 500k per year and who responded that they had: \n",
        "\n",
        "\"Participated in a full-time developer training program or bootcamp\"\n",
        "\n",
        "## Part 1 - Setting the Stage\n",
        "\n",
        "**1) Load the dataset**"
      ]
    },
    {
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      },
      "source": [
        "!wget https://raw.githubusercontent.com/ryanleeallred/datasets/master/bootcampers.csv"
      ],
      "execution_count": null,
      "outputs": []
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    {
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      "source": [
        "import pandas as pd\n",
        "import numpy as np \n",
        "import scipy.stats as stats\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "pd.set_option('display.max_rows', 100)\n",
        "pd.set_option('display.max_columns', 15)\n",
        "\n",
        "df = pd.read_csv('https://raw.githubusercontent.com/ryanleeallred/datasets/master/bootcampers.csv')\n",
        "print(df.shape)\n",
        "df.head(5)"
      ],
      "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"
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        {
          "output_type": "stream",
          "text": [
            "(2761, 15)\n"
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              "\n",
              "    .dataframe thead th {\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Unnamed: 0</th>\n",
              "      <th>Student</th>\n",
              "      <th>Employment</th>\n",
              "      <th>UndergradMajor</th>\n",
              "      <th>DevType</th>\n",
              "      <th>YearsCoding</th>\n",
              "      <th>YearsCodingProf</th>\n",
              "      <th>ConvertedSalary</th>\n",
              "      <th>EducationTypes</th>\n",
              "      <th>SelfTaughtTypes</th>\n",
              "      <th>TimeAfterBootcamp</th>\n",
              "      <th>LanguageWorkedWith</th>\n",
              "      <th>Gender</th>\n",
              "      <th>Age</th>\n",
              "      <th>RaceEthnicity</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>62</td>\n",
              "      <td>No</td>\n",
              "      <td>Employed full-time</td>\n",
              "      <td>Computer science, computer engineering, or sof...</td>\n",
              "      <td>Back-end developer;Data scientist or machine l...</td>\n",
              "      <td>12-14 years</td>\n",
              "      <td>6-8 years</td>\n",
              "      <td>120000.0</td>\n",
              "      <td>Taken an online course in programming or softw...</td>\n",
              "      <td>The official documentation and/or standards fo...</td>\n",
              "      <td>I already had a full-time job as a developer w...</td>\n",
              "      <td>C;F#;Haskell;Python;Scala</td>\n",
              "      <td>Male</td>\n",
              "      <td>25 - 34 years old</td>\n",
              "      <td>White or of European descent</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>73</td>\n",
              "      <td>No</td>\n",
              "      <td>Employed full-time</td>\n",
              "      <td>A humanities discipline (ex. literature, histo...</td>\n",
              "      <td>Back-end developer;Full-stack developer;System...</td>\n",
              "      <td>0-2 years</td>\n",
              "      <td>0-2 years</td>\n",
              "      <td>36000.0</td>\n",
              "      <td>Participated in a full-time developer training...</td>\n",
              "      <td>The official documentation and/or standards fo...</td>\n",
              "      <td>Four to six months</td>\n",
              "      <td>Java;JavaScript;SQL;HTML;CSS;Bash/Shell</td>\n",
              "      <td>Male</td>\n",
              "      <td>25 - 34 years old</td>\n",
              "      <td>White or of European descent</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>127</td>\n",
              "      <td>Yes, full-time</td>\n",
              "      <td>Employed full-time</td>\n",
              "      <td>A business discipline (ex. accounting, finance...</td>\n",
              "      <td>Full-stack developer</td>\n",
              "      <td>3-5 years</td>\n",
              "      <td>3-5 years</td>\n",
              "      <td>59980.0</td>\n",
              "      <td>Taken an online course in programming or softw...</td>\n",
              "      <td>The official documentation and/or standards fo...</td>\n",
              "      <td>One to three months</td>\n",
              "      <td>C#;JavaScript;TypeScript;HTML;CSS</td>\n",
              "      <td>Male</td>\n",
              "      <td>25 - 34 years old</td>\n",
              "      <td>East Asian</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>140</td>\n",
              "      <td>No</td>\n",
              "      <td>Employed full-time</td>\n",
              "      <td>A social science (ex. anthropology, psychology...</td>\n",
              "      <td>Data scientist or machine learning specialist;...</td>\n",
              "      <td>9-11 years</td>\n",
              "      <td>3-5 years</td>\n",
              "      <td>70000.0</td>\n",
              "      <td>Taken an online course in programming or softw...</td>\n",
              "      <td>Questions &amp; answers on Stack Overflow;Tapping ...</td>\n",
              "      <td>I haven’t gotten a developer job</td>\n",
              "      <td>JavaScript;Python;SQL;VBA</td>\n",
              "      <td>Male</td>\n",
              "      <td>25 - 34 years old</td>\n",
              "      <td>White or of European descent</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>153</td>\n",
              "      <td>No</td>\n",
              "      <td>Employed full-time</td>\n",
              "      <td>Computer science, computer engineering, or sof...</td>\n",
              "      <td>Mobile developer</td>\n",
              "      <td>6-8 years</td>\n",
              "      <td>3-5 years</td>\n",
              "      <td>105000.0</td>\n",
              "      <td>Taken an online course in programming or softw...</td>\n",
              "      <td>The official documentation and/or standards fo...</td>\n",
              "      <td>One to three months</td>\n",
              "      <td>C;Java;JavaScript;Objective-C;PHP;Python;Ruby;...</td>\n",
              "      <td>Male</td>\n",
              "      <td>25 - 34 years old</td>\n",
              "      <td>White or of European descent</td>\n",
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              "   Unnamed: 0         Student          Employment  \\\n",
              "0          62              No  Employed full-time   \n",
              "1          73              No  Employed full-time   \n",
              "2         127  Yes, full-time  Employed full-time   \n",
              "3         140              No  Employed full-time   \n",
              "4         153              No  Employed full-time   \n",
              "\n",
              "                                      UndergradMajor  \\\n",
              "0  Computer science, computer engineering, or sof...   \n",
              "1  A humanities discipline (ex. literature, histo...   \n",
              "2  A business discipline (ex. accounting, finance...   \n",
              "3  A social science (ex. anthropology, psychology...   \n",
              "4  Computer science, computer engineering, or sof...   \n",
              "\n",
              "                                             DevType  YearsCoding  \\\n",
              "0  Back-end developer;Data scientist or machine l...  12-14 years   \n",
              "1  Back-end developer;Full-stack developer;System...    0-2 years   \n",
              "2                               Full-stack developer    3-5 years   \n",
              "3  Data scientist or machine learning specialist;...   9-11 years   \n",
              "4                                   Mobile developer    6-8 years   \n",
              "\n",
              "  YearsCodingProf  ConvertedSalary  \\\n",
              "0       6-8 years         120000.0   \n",
              "1       0-2 years          36000.0   \n",
              "2       3-5 years          59980.0   \n",
              "3       3-5 years          70000.0   \n",
              "4       3-5 years         105000.0   \n",
              "\n",
              "                                      EducationTypes  \\\n",
              "0  Taken an online course in programming or softw...   \n",
              "1  Participated in a full-time developer training...   \n",
              "2  Taken an online course in programming or softw...   \n",
              "3  Taken an online course in programming or softw...   \n",
              "4  Taken an online course in programming or softw...   \n",
              "\n",
              "                                     SelfTaughtTypes  \\\n",
              "0  The official documentation and/or standards fo...   \n",
              "1  The official documentation and/or standards fo...   \n",
              "2  The official documentation and/or standards fo...   \n",
              "3  Questions & answers on Stack Overflow;Tapping ...   \n",
              "4  The official documentation and/or standards fo...   \n",
              "\n",
              "                                   TimeAfterBootcamp  \\\n",
              "0  I already had a full-time job as a developer w...   \n",
              "1                                 Four to six months   \n",
              "2                                One to three months   \n",
              "3                   I haven’t gotten a developer job   \n",
              "4                                One to three months   \n",
              "\n",
              "                                  LanguageWorkedWith Gender  \\\n",
              "0                          C;F#;Haskell;Python;Scala   Male   \n",
              "1            Java;JavaScript;SQL;HTML;CSS;Bash/Shell   Male   \n",
              "2                  C#;JavaScript;TypeScript;HTML;CSS   Male   \n",
              "3                          JavaScript;Python;SQL;VBA   Male   \n",
              "4  C;Java;JavaScript;Objective-C;PHP;Python;Ruby;...   Male   \n",
              "\n",
              "                 Age                 RaceEthnicity  \n",
              "0  25 - 34 years old  White or of European descent  \n",
              "1  25 - 34 years old  White or of European descent  \n",
              "2  25 - 34 years old                    East Asian  \n",
              "3  25 - 34 years old  White or of European descent  \n",
              "4  25 - 34 years old  White or of European descent  "
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      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "**2) Select two random samples from this dataset, one with a sample size of 20 and the other with a sample size of 200. (Use a `random_state` of `42` when selecting the samples)**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m1vuFGxVQo64",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "sample1 = df.sample(20, random_state=42)\n",
        "sample2 = df.sample(200, random_state=42)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y2Rz-8O-YmF9",
        "colab_type": "text"
      },
      "source": [
        "**3) Calculate and report the sample means of the `ConvertedSalary` column for both of the samples.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ti9x37XSQ_yL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x_bar_sample1 = sample1['ConvertedSalary'].mean()\n",
        "x_bar_sample1\n",
        "\n",
        "x_bar_sample2 = sample2['ConvertedSalary'].mean()\n",
        "x_bar_sample2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AtGASqgxYp5t",
        "colab_type": "text"
      },
      "source": [
        "**4) Both of these sample means are estimates of an underlying population value. Which sample mean do you trust more? Why? Would a non-technical audience have any idea about which of these values is more trustworthy?**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "I would trust sample 2 more because of the bigger sample size. A non-technical audience will not know about one of the two samples being better."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-2ulIAGmYudp",
        "colab_type": "text"
      },
      "source": [
        "**5) Does just the point estimate (individual value of the sample mean) indicate to you anything about how much sampling error there could be with these estimates?**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hD5HloatYxoh",
        "colab_type": "text"
      },
      "source": [
        "The point estimate does not indicate much about any possible sampling error in the estimates"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SpqgKQfTYvF0",
        "colab_type": "text"
      },
      "source": [
        "**6) What strategies could we use when reporting these numbers to not only report our estimates but also to give non-technical readers an idea about how far off our estimates might be due to sampling error?**\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h7N1WnTTYyD7",
        "colab_type": "text"
      },
      "source": [
        "we could use confidence intervals or margin of error to give non-technical readers an idea about how far off our estimates might be due to the sampling error.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9tIHBlM_SyGR",
        "colab_type": "text"
      },
      "source": [
        "## Part 2 - Reporting CIs / MOEs along with our point estimates for more context.\n",
        "\n",
        "**1) Calculate and report a 95% confidence interval around both of the sample means from part 1.**\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hfCO0gHEUOrE",
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      "source": [
        "def confidence_interval(sample, confidence_int):\n",
        "\n",
        "# to make sure we get an array \n",
        "  data = np.array(sample)\n",
        "\n",
        "# Confidence_interval = x_bar +- t*(s/sgrt(n))\n",
        "\n",
        "# calculating std dev(s) on the sample and sqrt of the sample size(n)\n",
        "  s = np.std(data, ddof=1)\n",
        "  n = np.sqrt(data.shape[0])\n",
        "\n",
        "# calculating t using stats \n",
        "  t = stats.t.ppf((1-(1-confidence_int)/2), n-1)\n",
        "\n",
        "# calculating margin of error t*(s/sgrt(n))\n",
        "  moe = t * ( s / np.sqrt(n) )\n",
        "\n",
        "# calculating mean of the sample \n",
        "  x_bar = data.mean()\n",
        "\n",
        "  upper_bound = x_bar + moe\n",
        "  lower_bound = x_bar - moe \n",
        "\n",
        "  return(upper_bound, x_bar, lower_bound, moe)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r5OqA6GYUbUZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# with 20 samples \n",
        "CI_sample1 = confidence_interval(sample1['ConvertedSalary'], 0.95)\n",
        "CI_sample1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kvtuhUzzUlqH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# with 200 samples\n",
        "CI_sample2 = confidence_interval(sample2['ConvertedSalary'], 0.95)\n",
        "CI_sample2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vdiW7DHRZwK-",
        "colab_type": "text"
      },
      "source": [
        "**2) Which confidence interval is wider and why?**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p5KGlyvYZ1Qq",
        "colab_type": "text"
      },
      "source": [
        "The confidence interval of the first sample is much wider. Due to its lower sample size the standard error of our estimate is bigger causing the distribution of the sample means to be wider."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6N33K4NvZ13H",
        "colab_type": "text"
      },
      "source": [
        "**3) Report the mean and the margin of error for both of the sample means. What does the Margin of Error Represent?**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MfMIBftMU_rz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "mean_moe_sample1 = confidence_interval(sample1['ConvertedSalary'], 0.95)\n",
        "print(f'Sample Mean: {mean_moe_sample1[1]}\\nMargin Error: {mean_moe_sample1[3]}')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DOJ41W1tVWa6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "mean_moe_sample2 = confidence_interval(sample2['ConvertedSalary'], 0.95)\n",
        "print(f'Sample Mean: {mean_moe_sample2[1]}\\nMargin Error: {mean_moe_sample2[3]}')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_7NuYtHfaQav",
        "colab_type": "text"
      },
      "source": [
        "The margin of error gives an idea of how far off our estimates might be."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zkg9EW9KTgGv",
        "colab_type": "text"
      },
      "source": [
        "## Part 3 - Communicate the Precision of Sample Estimates Graphically\n",
        "\n",
        "**1) Create a plot using `plt.errorbar` that compares both of the confidence intervals.** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2QOQGVfsVfFZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "plt.style.use('fivethirtyeight')\n",
        "plt.errorbar(0, CI_sample1[1], yerr=CI_sample1[3], fmt='o', label='Sample1')\n",
        "plt.errorbar(1, CI_sample2[1], yerr=CI_sample2[3], fmt='o', label='Sample2')\n",
        "plt.ylabel('Converted Salary')\n",
        "plt.legend(loc='upper center')\n",
        "plt.title('Confidence intervals for Converted Salary')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HsTtONTNawFi",
        "colab_type": "text"
      },
      "source": [
        "**2) Create a plot using `plt.bar` that compares both of the confidence intervals.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UE1fxaoKW1Xg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "plt.style.use('fivethirtyeight')\n",
        "plt.bar(0, height=CI_sample1[1], yerr=CI_sample1[3], label='Sample1', color='lightgreen')\n",
        "plt.bar(1, height=CI_sample2[1], yerr=CI_sample2[3], label='Sample2', color='lightblue')\n",
        "plt.ylabel('Converted Salary')\n",
        "plt.legend(loc='upper center')\n",
        "plt.title('Confidence intervals for Converted Salary')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZGCzS-BFctob",
        "colab_type": "text"
      },
      "source": [
        "## Part 4 - Check for Understanding\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E181afPXezJ9",
        "colab_type": "text"
      },
      "source": [
        "**Calculate a Confidence Interval using the entire dataset. How precise do our estimates get?**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3puy99D6esLn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# calling out the confidence_interval function on the entire dataset\n",
        "CI_df = confidence_interval(df['ConvertedSalary'], .95)\n",
        "CI_df"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wbA0inEKexdW",
        "colab_type": "text"
      },
      "source": [
        "**What does \"precision\" mean in the context of statistical estimates and how is that different from \"accuracy?\"**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Btl5phUUd6L4",
        "colab_type": "text"
      },
      "source": [
        "Precision means how tight the confidence is around the point estimate.\n",
        "Accuracy means how close are the estimates to the true value"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4F-4ux7sd5pL",
        "colab_type": "text"
      },
      "source": [
        "**It is very common to misunderstand what is captured by a 95% confidence interval. What is the correct interpretation? ([Hint](https://www.statisticssolutions.com/misconceptions-about-confidence-intervals/))**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bSU07naHd6li",
        "colab_type": "text"
      },
      "source": [
        "95% of the confidence intervals calculated from the random samples will contain the true population mean. If done 100 times, it is to be expected that 95 out of those 100 confidence intervals will have the true population mean."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cvtnsGLJa4bW",
        "colab_type": "text"
      },
      "source": [
        "# Stretch Goals:\n",
        "\n",
        "1) Study the relationship between t-tests and confidence intervals.\n",
        " - Find a sample mean that we have worked with and construct a 95% confidence interval around it. (find the lower and upper bounds)\n",
        " - Run a 1-sample t-test with the null hypothesis value being just barely **outside** of the confidence interval. What is the p-value?\n",
        " - Run a 1-sample t-test with the null hypothesis value being just barely **inside** of the confidence interval. What is the p-value?\n",
        "\n",
        "  What does it mean when we say that the boundaries of the confidence interval are the boundaries of statistical significance in a 1-sample t-test?\n",
        "\n",
        "\n",
        "2) Go back to our [congressional voting dataset](https://archive.ics.uci.edu/ml/datasets/Congressional+Voting+Records) and build confidence intervals around the means of all of the issues for a single party. Compare all of those confidence intervals graphically on a single graph. \n",
        "\n",
        "3) Dive deeper into the [2018 Stack Overflow Survey](https://www.kaggle.com/stackoverflow/stack-overflow-2018-developer-survey) results to see what cool things you can find."
      ]
    }
  ]
}