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.

1. State the null and alternative hypotheses
2. Find the t-statistics
3. Find the critical value
4. Construct a 90% confidence interval for the difference between the two means
5. Does the diet appear to be effective in reducing weight?

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