1. A national chain of health clubs says the mean amount of weight lost by members during the past month was at least 5 pounds. Skeptical of this claim, a consumer advocate believes the chain's assertion is an exaggeration. She interviews a random sample of 40 members, finding their mean weight loss to be 4.6 pounds, with a standard deviation of 1.5 pounds. At the 0.01 level of significance, evaluate the health club's contention.

2. In an interview with a local newspaper,  a respected trial lawyer claims that he wins at least 75% of his court cases. Bert, a skeptical statistics student, sets up a one-tail test at the 0.05 level of significance to evaluate the attorney's claim. The student plans to examine a ran- dom sample of 40 cases tried by the attorney and deter- mine the proportion of these cases that were won. The null and alternative hypotheses are H0: 7T $ 0.75 and H1: 7T , 0.75. Using the techniques of this chapter, Bert sets up a hypothesis test in which the decision rule is "Reject H0 if z , 21.645, otherwise do not reject." What is the probability that Bert will make a Type II error (fail to reject a false null hypothesis) if the attor- ney's true population proportion of wins is actually

a. 7T 5 0.75?

b. 7T 5 0.70?

c. 7T 5 0.65?

d.  7T 5 0.60?          

e. 7T 5 0.55?

f. Making use of the probabilities calculated in parts

(a)   through (e), describe and plot the power curve for Bert's hypothesis test.