Data_Analyst_ND_Project0.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Chopsticks!\n",
    "\n",
    "A few researchers set out to determine the optimal length of chopsticks for children and adults. They came up with a measure of how effective a pair of chopsticks performed, called the \"Food Pinching Performance.\" The \"Food Pinching Performance\" was determined by counting the number of peanuts picked and placed in a cup (PPPC).\n",
    "\n",
    "### An investigation for determining the optimum length of chopsticks.\n",
    "[Link to Abstract and Paper](http://www.ncbi.nlm.nih.gov/pubmed/15676839)  \n",
    "*the abstract below was adapted from the link*\n",
    "\n",
    "Chopsticks are one of the most simple and popular hand tools ever invented by humans, but have not previously been investigated by [ergonomists](https://www.google.com/search?q=ergonomists). Two laboratory studies were conducted in this research, using a [randomised complete block design](http://dawg.utk.edu/glossary/whatis_rcbd.htm), to evaluate the effects of the length of the chopsticks on the food-serving performance of adults and children. Thirty-one male junior college students and 21 primary school pupils served as subjects for the experiment to test chopsticks lengths of 180, 210, 240, 270, 300, and 330 mm. The results showed that the food-pinching performance was significantly affected by the length of the chopsticks, and that chopsticks of about 240 and 180 mm long were optimal for adults and pupils, respectively. Based on these findings, the researchers suggested that families with children should provide both 240 and 180 mm long chopsticks. In addition, restaurants could provide 210 mm long chopsticks, considering the trade-offs between ergonomics and cost.\n",
    "\n",
    "### For the rest of this project, answer all questions based only on the part of the experiment analyzing the thirty-one adult male college students.\n",
    "Download the [data set for the adults](https://www.udacity.com/api/nodes/4576183932/supplemental_media/chopstick-effectivenesscsv/download), then answer the following questions based on the abstract and the data set.\n",
    "\n",
    "**If you double click on this cell**, you will see the text change so that all of the formatting is removed. This allows you to edit this block of text. This block of text is written using [Markdown](http://daringfireball.net/projects/markdown/syntax), which is a way to format text using headers, links, italics, and many other options. You will learn more about Markdown later in the Nanodegree Program. Hit shift + enter or shift + return to show the formatted text."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. What is the independent variable in the experiment?\n",
    "chop stick length\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. What is the dependent variable in the experiment?\n",
    "food-pinching performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. How is the dependent variable operationally defined?\n",
    "The dependent variable is defined by the number of peanuts picked and placed in a cup (PPPC)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Based on the description of the experiment and the data set, list at least two variables that you know were controlled.\n",
    "sex (all male), education\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One great advantage of ipython notebooks is that you can document your data analysis using code, add comments to the code, or even add blocks of text using Markdown. These notebooks allow you to collaborate with others and share your work. For now, let's see some code for doing statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# pandas is a software library for data manipulation and analysis\n",
    "# We commonly use shorter nicknames for certain packages. Pandas is often abbreviated to pd.\n",
    "# hit shift + enter to run this cell or block of code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Food.Pinching.Efficiency</th>\n",
       "      <th>Individual</th>\n",
       "      <th>Chopstick.Length</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19.55</td>\n",
       "      <td>1</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>27.24</td>\n",
       "      <td>2</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28.76</td>\n",
       "      <td>3</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>31.19</td>\n",
       "      <td>4</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21.91</td>\n",
       "      <td>5</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>27.62</td>\n",
       "      <td>6</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>29.46</td>\n",
       "      <td>7</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>26.35</td>\n",
       "      <td>8</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>26.69</td>\n",
       "      <td>9</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>30.22</td>\n",
       "      <td>10</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>27.81</td>\n",
       "      <td>11</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>23.46</td>\n",
       "      <td>12</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>23.64</td>\n",
       "      <td>13</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>27.85</td>\n",
       "      <td>14</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>20.62</td>\n",
       "      <td>15</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>25.35</td>\n",
       "      <td>16</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>28.00</td>\n",
       "      <td>17</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>23.49</td>\n",
       "      <td>18</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>27.77</td>\n",
       "      <td>19</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>18.48</td>\n",
       "      <td>20</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>23.01</td>\n",
       "      <td>21</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>22.66</td>\n",
       "      <td>22</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>23.24</td>\n",
       "      <td>23</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>22.82</td>\n",
       "      <td>24</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>17.94</td>\n",
       "      <td>25</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>26.67</td>\n",
       "      <td>26</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>28.98</td>\n",
       "      <td>27</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>21.48</td>\n",
       "      <td>28</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>14.47</td>\n",
       "      <td>29</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>28.29</td>\n",
       "      <td>30</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156</th>\n",
       "      <td>26.18</td>\n",
       "      <td>2</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>157</th>\n",
       "      <td>25.93</td>\n",
       "      <td>3</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158</th>\n",
       "      <td>28.61</td>\n",
       "      <td>4</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>159</th>\n",
       "      <td>20.54</td>\n",
       "      <td>5</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>26.44</td>\n",
       "      <td>6</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>161</th>\n",
       "      <td>29.36</td>\n",
       "      <td>7</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>162</th>\n",
       "      <td>19.77</td>\n",
       "      <td>8</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>163</th>\n",
       "      <td>31.69</td>\n",
       "      <td>9</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>164</th>\n",
       "      <td>24.64</td>\n",
       "      <td>10</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>22.09</td>\n",
       "      <td>11</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>166</th>\n",
       "      <td>23.42</td>\n",
       "      <td>12</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>167</th>\n",
       "      <td>28.63</td>\n",
       "      <td>13</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>168</th>\n",
       "      <td>26.30</td>\n",
       "      <td>14</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>22.89</td>\n",
       "      <td>15</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>170</th>\n",
       "      <td>22.68</td>\n",
       "      <td>16</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>30.92</td>\n",
       "      <td>17</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>172</th>\n",
       "      <td>20.74</td>\n",
       "      <td>18</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>27.24</td>\n",
       "      <td>19</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>17.12</td>\n",
       "      <td>20</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>23.63</td>\n",
       "      <td>21</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>20.91</td>\n",
       "      <td>22</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>23.49</td>\n",
       "      <td>23</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>24.86</td>\n",
       "      <td>24</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>16.28</td>\n",
       "      <td>25</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>21.52</td>\n",
       "      <td>26</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>27.22</td>\n",
       "      <td>27</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>17.41</td>\n",
       "      <td>28</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>16.42</td>\n",
       "      <td>29</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>28.22</td>\n",
       "      <td>30</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>27.52</td>\n",
       "      <td>31</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>186 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Food.Pinching.Efficiency  Individual  Chopstick.Length\n",
       "0                       19.55           1               180\n",
       "1                       27.24           2               180\n",
       "2                       28.76           3               180\n",
       "3                       31.19           4               180\n",
       "4                       21.91           5               180\n",
       "5                       27.62           6               180\n",
       "6                       29.46           7               180\n",
       "7                       26.35           8               180\n",
       "8                       26.69           9               180\n",
       "9                       30.22          10               180\n",
       "10                      27.81          11               180\n",
       "11                      23.46          12               180\n",
       "12                      23.64          13               180\n",
       "13                      27.85          14               180\n",
       "14                      20.62          15               180\n",
       "15                      25.35          16               180\n",
       "16                      28.00          17               180\n",
       "17                      23.49          18               180\n",
       "18                      27.77          19               180\n",
       "19                      18.48          20               180\n",
       "20                      23.01          21               180\n",
       "21                      22.66          22               180\n",
       "22                      23.24          23               180\n",
       "23                      22.82          24               180\n",
       "24                      17.94          25               180\n",
       "25                      26.67          26               180\n",
       "26                      28.98          27               180\n",
       "27                      21.48          28               180\n",
       "28                      14.47          29               180\n",
       "29                      28.29          30               180\n",
       "..                        ...         ...               ...\n",
       "156                     26.18           2               330\n",
       "157                     25.93           3               330\n",
       "158                     28.61           4               330\n",
       "159                     20.54           5               330\n",
       "160                     26.44           6               330\n",
       "161                     29.36           7               330\n",
       "162                     19.77           8               330\n",
       "163                     31.69           9               330\n",
       "164                     24.64          10               330\n",
       "165                     22.09          11               330\n",
       "166                     23.42          12               330\n",
       "167                     28.63          13               330\n",
       "168                     26.30          14               330\n",
       "169                     22.89          15               330\n",
       "170                     22.68          16               330\n",
       "171                     30.92          17               330\n",
       "172                     20.74          18               330\n",
       "173                     27.24          19               330\n",
       "174                     17.12          20               330\n",
       "175                     23.63          21               330\n",
       "176                     20.91          22               330\n",
       "177                     23.49          23               330\n",
       "178                     24.86          24               330\n",
       "179                     16.28          25               330\n",
       "180                     21.52          26               330\n",
       "181                     27.22          27               330\n",
       "182                     17.41          28               330\n",
       "183                     16.42          29               330\n",
       "184                     28.22          30               330\n",
       "185                     27.52          31               330\n",
       "\n",
       "[186 rows x 3 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = r'/Volumes/Transcend/Udacity/Data-Analyst/1/chopstick-effectiveness.csv'\n",
    "# Change the path to the location where the chopstick-effectiveness.csv file is located on your computer.\n",
    "# If you get an error when running this block of code, be sure the chopstick-effectiveness.csv is located at the path on your computer.\n",
    "\n",
    "dataFrame = pd.read_csv(path)\n",
    "dataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do a basic statistical calculation on the data using code! Run the block of code below to calculate the average \"Food Pinching Efficiency\" for all 31 participants and all chopstick lengths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25.00559139784947"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataFrame['Food.Pinching.Efficiency'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This number is helpful, but the number doesn't let us know which of the chopstick lengths performed best for the thirty-one male junior college students. Let's break down the data by chopstick length. The next block of code will generate the average \"Food Pinching Effeciency\" for each chopstick length. Run the block of code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chopstick.Length</th>\n",
       "      <th>Food.Pinching.Efficiency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>180</td>\n",
       "      <td>24.935161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>210</td>\n",
       "      <td>25.483871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>240</td>\n",
       "      <td>26.322903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>270</td>\n",
       "      <td>24.323871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>300</td>\n",
       "      <td>24.968065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>330</td>\n",
       "      <td>23.999677</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Chopstick.Length  Food.Pinching.Efficiency\n",
       "0               180                 24.935161\n",
       "1               210                 25.483871\n",
       "2               240                 26.322903\n",
       "3               270                 24.323871\n",
       "4               300                 24.968065\n",
       "5               330                 23.999677"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meansByChopstickLength = dataFrame.groupby('Chopstick.Length')['Food.Pinching.Efficiency'].mean().reset_index()\n",
    "meansByChopstickLength\n",
    "\n",
    "# reset_index() changes Chopstick.Length from an index to column. Instead of the index being the length of the chopsticks, the index is the row numbers 0, 1, 2, 3, 4, 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Which chopstick length performed the best for the group of thirty-one male junior college students?\n",
    "240 mm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1122d24e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Causes plots to display within the notebook rather than in a new window\n",
    "%pylab inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(x=meansByChopstickLength['Chopstick.Length'], y=meansByChopstickLength['Food.Pinching.Efficiency'])\n",
    "            # title=\"\")\n",
    "plt.xlabel(\"Length in mm\")\n",
    "plt.ylabel(\"Efficiency in PPPC\")\n",
    "plt.title(\"Average Food Pinching Efficiency by Chopstick Length\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6. Based on the scatterplot created from the code above, interpret the relationship you see. What do you notice?\n",
    "\n",
    "The performance gets better from 180 mm, to 210 mm and 240 mm, with 240 mm being the length with the best performance. It then drops down with chopsticks of 270 mm, incresing again at 300 mm. The lowest result is for chopsticks with a length of 330 mm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In the abstract the researchers stated that their results showed food-pinching performance was significantly affected by the length of the chopsticks, and that chopsticks of about 240 mm long were optimal for adults.\n",
    "\n",
    "#### 7a. Based on the data you have analyzed, do you agree with the claim?\n",
    "Yes.\n",
    "\n",
    "#### 7b. Why?\n",
    "The operational definition was well chosen with counting the number of peanuts picked. Therefore we can assume that the results measure what we wanted to measure. As the best results were measured for 240 mm chopsticks, I can agree with the claim. \n",
    "\n",
    "However, it's still interesting that the efficiency with chopsticks with a length of 300 mm is better than with chopsticks of 270 and 330 mm.\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}