Pete’s Powerful Pills ( PPP) has branched out and is now promoting a vaccine which is supposed to prevent statisticitis, a nasty disease afflicting students at the local Evermore University. They are trying to convince the University’s Health Center that the vaccine is worth stocking. The campus Health Center has agreed to stock and administer the vaccine if it sells well enough, at least =50 vaccines per week. PPP arranges for the Health Center to conduct a 36 week trial with the goal of convincing the Center to stock the vaccine. They find that the Center has administered an average of Xbar = 55 vaccines per week over the period with a standard deviation of s= 6.99.(Note: Since n > 30, we can use the z-distribution)

(a). Compute a 95% confidence interval for ., the mean number of vaccines the Health Center will administer per week in the long run. Does it look like the Health Center will be willing to stock the vaccine? Explain.

(b). Perform the hypothesis test using the critical value approach. Use the right tail option of the alternative hypothesis and do all the steps I show you in class in order to arrive at your conclusion.

(c). Perform the hypothesis test using the p- value approach. Use the right tail option of the alternative hypothesis and do all the steps I show you in class in order to arrive at your conclusion.

(d). Are the results from part (b) and part(c) consistent with each other?

(e). Suppose that PPP makes a $5 profit on every vaccine administered by the Health Center. Furthermore, suppose they need to average profits of at least $260 per week for it to be worthwhile to market the vaccine at the School. Can they be 95% (really 97.5%) sure of meeting their goal? Explain [Hint, Use the C .I computed in part (a)]