When the draft lottery for military service in the Vietnam War was conducted, officials "randomly" selected birthdays. For example, September 14 was selected first, and that date was assigned the rank of 1. If March 7 were selected second, it would be assigned the rank of 2. This meant that all eligible men with birthdays on September 14 were drafted first, and men with birthdays on March 7 were selected next. If the birthdays were selected truly at random, the mean rank for each month should be about the same as that of any other month. The output shown below compares the mean ranks for each month. Small values mean the people born in that month were more likely to be called up.

a. Which month had the smallest mean?
b. Test the hypothesis that the population means are equal for all twelve months. Show all four steps for ANOVA. Do not-do post-hoc comparisons. Use a significance level of 0.05.

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One-way ANOVA: Jan, Feb, Mar, Apr, May, Jun, 5 6 Jul, Aug, Sep, oct, Nov, Dec Source DE Factor 11 29050 26410 2.46 0.006 Error 354 3795120 10721 Total 35 4085628 Level NMean StDev 99.7 29 203.0 104. 0 95.8 30 203. 109.4 31 208.0 115. 0 30 195.7 117.9 31 181.5 109. 6 31 173.5 112.7 87.2 96.8 94.4 95.1 31 201.2 31 225.8 Apr kay 30 157.3 31 182.5 30 148.7 31 121.5