Section 12.1 Learning Check|Use the following to answer questions 1-6.<br> At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experients between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep to crawl a distance of four feet within one minute. the resulting data were grouped by month of birth. The data are for January, May, and September.<br><table border=3><tr><td>Birth Month</td><td>Average Crawling Age</td><td>Standard Deviation</td><td>n</td></tr><tr><td>January</td><td>29.84</td><td>7.08</td><td>32</td></tr><tr><td>May</td><td>28.58</td><td>8.07</td><td>27</td></tr><tr><td>September</td><td>33.83</td><td>6.93</td><td>38</td></tr></table><br>Crawling age is given in weeks. Assume the data are 3 independent SRS's, one from each of the 3 populations (babies born in a particular month) and that the populations of crawling ages have normal distributions.<br>A partial ANOVA table is given below.<br><table border=3><tr><td>Dource</td><td>df</td><td>Sums of Squares</td><td>Mean Square</td><td>F-ratio</td></tr><tr><td>Birth Month</td><td> </td><td>505.26</td><td> </td> <td> </td></tr><tr><td>Error</td><td> </td><td> </td> <td>53.45</td><td> </td></tr><tr><td>Total</td><td> </td><td> </td><td> </td> <td> </td></tr></table><br>|Please enter your Full Name:|Your Email Address:|Your ID Number or Password:|The degrees of freedom for birth month (group) are # 2 %% 3 %% 94 %% 97 %%|The degrees of freedom for error are # 2 %% 3 %% 94 %% 97 %%|The null hypothesis for the ANOVA F-test is that the population mean crawling ages are equal for all three birth months. The alternative is # that the population mean crawling age is larger for January that for the other two months %% that the population mean crawling age is larger for May than for the other two months %% that the population mean crawling age is larger for September than for the other two months %% none of the above %%|The value of the ANOVA F-statistic for testing equlaity of the population means of the 3 birth months is # 3.15 %% 4.73 %% 6.30 %% 9.45 %%|The P-value for the ANOVA F-test for testing equlaity of the population means of the 3 birth months is # less than 0.001 %% between 0.001 and 0.010 %% between 0.010 and 0.025 %% greater than 0.025 %%|Multiple comparison procedures are going to be done using the Benferroni method with alpha 0.10. The value of t** is 2.1598. The MSD (minimum significant difference) for finding a difference between January and May is # -1.26 %% 1.91 %% 1.26 %% 4.13 %%