Shoplifting in the U. S. costs retailers about $15 billion a year. Those losses translate into higher prices for consumers. Despite the seriousness of the problem, Shoplifters Alternative of Jericho, N. Y., claims that only 50% of all shoplifters are turned over to police (Athens Daily News, Dec. 12,1999). A random sample of 40 U. S.

retailers were questioned concerning the disposition of the most recent shoplifter they apprehended. Only 24 were turned over to police. Do these data provide sufficient evidence to contradict Shoplifters Alternative?

a. Is the sample size large enough to use thc inferential procedure presented in this section to answer the question? Explain.

b. Conduct a hypothesis test to answer the question of interest. Use a = .05.

c. Find the observed significance level of the hypothesis test in part b.

d. For what values of a would the observed significance level be sufficient to reject the null hypothesis of the test you conducted in part b?

659 The placebo effect describes the phenomenon of improvement in the condition of a patient taking a placebo-a pill that looks and tastes real but contains no medically active chemicals. Physicians at a clinic in La Jolla, California, gave what they thought were drugs to 7,000 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 70% of the patients reported an improved condition (Forbes, May 22,1995). Use this information to test (at a = .05) the placebo effect at the clinic.

Assume that if the placebo is ineffective, the probability of a patient's condition improving is .5.