Question: Researchers obtained weight loss data from a sample of dieters. The before and after weights of 12 subjects are recorded and the differences are computed. These differences have a mean of \(\bar{D}=133.75\) pounds, and a standard deviation of \({{s}_{d}}=17.07\) pounds. Test the claim at the 0.05 significance level that the diet is an effective method of losing weight.

(a) State the null and alternative hypotheses

(b) Find the t-statistics

(c) Find the critical value

(d) Construct a 90% confidence interval for the difference between the two means

(e) Does the diet appear to be effective in reducing weight?