A researcher wanted to investigate the eject of a special diet on lowering blood pressure. She chose a random sample of 16 adults. 8 of the adults chosen were then chosen at random and put on the dietary plan for 6 months. The other 8 adults were on a normal diet for 6 months. The following table gives the blood pressure of the 16 adults at the end of the 6-month period.
Special diet 102 127 118 130 115 107 124 126
Normal diet 128 120 138 109 123 132 119 129
a. Let u0 and u1 be the population means blood pressure of adults on the special and normal diets, respectively. State the null and alternative hypotheses that the researcher is interested in testing.
b. Should the matched-pair t-procedure be used to analyze the data? Explain.
c. Let sigma0 squared and sigma1 squared denote the population variance of adults on the special and normal diets, respectively. Do the data provide any evidence that the two population variances are different? Give evidence to support your answer.
d. Regardless of your answer in part (c), suppose now that the researcher is willing to make an assumption that the two population variances are the same. By re-expressing the hypotheses in part (a) in terms of one parameter u0 minus u1 (i.e., the difference between the two original parameters), perform the test by constructing the 90% CI for the parameter. State your conclusion.