1. State the full model, including the necessary assumptions, and define all of your notation.
2. Estimate the five treatment effects, and show that they sum to zero.
3. Determine the value of the standardized test statistic (i.e., the F-statistic), the numerator degrees of freedom, and the denominator degrees of freedom.

Scientists are interested in whether the energy costs involved in reproduc- tion affect longevity. In this experiment, 125 male fruit flies were divided at random into five sets of 25. In one group, the males were kept by themselves. In two groups, the males were supplied with one or eight receptive virgin fe- male fruit flies per day. In the final two groups, the males were supplied with one or eight unreceptive (pregnant) female fruit flies per day. Other than the number and type of companions, the males were treated identically. The longevity of the flies was observed. Data from Hanley and Shapiro (1994). Companions Longevity (days) None 35 37 49 46 63 39 46 56 63 65 56 65 70 63 65 70 77 81 86 70 70 77 77 81 77 1 pregnant 40 37 44 47 47 47 68 47 54 61 71 75 89 58 59 62 79 96 58 62 70 72 75 96 75 1 virgin 46 42 65 46 58 42 48 58 50 80 63 65 70 70 72 97 46 56 70 70 72 76 90 76 92 8 pregnant 21 40 44 54 36 40 56 60 48 53 60 60 65 68 60 81 81 48 48 56 68 75 81 48 68 8 virgin 16 19 19 32 33 33 30 42 42 33 26 30 40 54 34 34 47 47 42 47 54 54 56 60 44