*15. In Example 2 in this chapter, we tested to see whether dieters and exercisers had significantly different average fat loss. We concluded that they did because the difference for the samples under consideration was 1.8 kg, with a measure of uncertainty of 0.83 kg and a standardized score of 2.17. Fat loss was higher for the dieters.

a. Construct a 95% confidence interval for the population difference in mean fat loss. Consider the two different methods for presenting results: (1) the p-value and conclusion from the hypothesis test or (2) the confidence interval.

Which do you think is more informative? Explain.

*b. Suppose the alternative hypothesis had been that men who exercised lost more fat on average than men who dieted. Would the null hypothesis have been rejected? Explain why or why not. If yes, give the p-value that would have been used.

c. Suppose the alternative hypothesis had been that men who dieted lost more fat on average than men who exercised. Would the null hypothesis have been rejected? Explain why or why not. If yes, give the p-value that would have been used.