Question: (18 points) Assume we have a study with 5 treatment groups, each group representing different doses of a headache drug of interest. The doses are 0 mg (control group), 200 mg, 300 mg, 400 mg, and 500 mg. The main response is reduction in pain, following start of treatment, which is considered a continuous measurement. Originally, 75 participants were randomized equally to each group (i.e., 15 to each group), but before the study actually began, 2 people dropped out of the 0 mg group, 1 person dropped out of the 200 mg group, 0 people dropped out of the 300 mg group, 3 people dropped out of the 400 mg group, and 4 people dropped out of the 500 mg group. For the following questions, take this dropout information into consideration regarding each group’s sample size.
a.(2 points) Write out the appropriate null and alternative hypothesis for comparing all treatment groups on mean reduction in pain.
b.(6 points) (i) What is the appropriate estimate of σ2 in this study (in naMeand formula only, noting you cannot calculate it without raw data or summary statistics on the response), and (ii) What are the degrees of freedom associated with this estimate?
c.(6 points) (i) What is the appropriate statistic to carry out the test in (a). Again, as with (b), because of lack of data provided, you cannot actually calculate this statistic. (ii) What distribution does this statistic follow, including the appropriate degrees of freedom?
d.(4 points) Say the null hypothesis in (a) was rejected, and we decide to perform the following comparisons: (200 vs. 0, 300 vs. 0, 400 vs. 0, and 300 vs. 200 mg). If we start out with an initial α=.10, what is the proper comparison-wise error rate for each of these comparisons, using the Bonferroni adjustment?
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