When 40 people use the weight watchers diet for one year, their mean weight loss was 3.0 pounds. historically the standard deviation is σ = 4.9 pounds (based on data from "comparison of the atkins, ornish, weight watchers, and zone diets for weight loss and heart disease reduction," by dansinger, et al., journal of the american medical association, vol. 293, no. 1). use a 0.01 significance level to test the claim that the mean weight loss is greater than 0.

a) state the null and alternate hypotheses. (hint: µ = 0)

b) would you perform a left-tailed, right-tailed or two-tailed test? why?

c) compute the test statistic.

d) determine the p-value. (this one is tricky! )

e) would you reject or fail to reject the null hypothesis?

f) interpret your conclusion in the context of this problem.

g) calculate a 99% confidence interval for the average number of pounds lost on this diet. does this interval support your conclusion from your hypothesis test? explain.