Suppose a large-scale randomized experiment were conducted to compare two weight loss plans. At the end of the experiment, the weight loss for each subject (in pounds) was recorded. The p-value turned out to be .004, and a 99% confidence interval for the difference in means turned out to be (0.26, 0.84).
a. Do the data provide strong evidence that the mean weight loss differs between the two plans? Explain briefly.
b. Do the data provide strong evidence that the mean weight loss differs considerably (i.e., a lot) between the two plans? Explain briefly.
c. Describe briefly what a Type II error would mean in this context.
d. Describe briefly what a Type I error would mean in this context.