Question: Although we have not emphasized it, the paired t-test can be used to test hypotheses in which the null value is something other than 0. For example, suppose that the proponents of a diet plan claim that the mean amount of weight lost in the first 3 weeks of following the plan is 10 pounds. A consumer advocacy group is skeptical and measures the beginning and ending weights for a random sample of 20 people who follow the plan for 3 weeks. The mean and standard deviation for the difference in weight at the two times are 8 pounds and 4 pounds, respectively.
a. What is the parameter of interest? Be sure to specify the appropriate population.
b. What are the null and alternative hypotheses?
c. What is the value of the test statistic?
d. What is the p-value for the test?
e. What conclusion can the consumer advocacy group make? Use a = .05.