Refer to Exercise 7.134.
Shoplifting in the United States costs retailers about $35 million a day. Despite the seriousness of the problem, the National Association of shoplifting Prevention (NASP) claims that only 50% of all shoplifters are turned over to police (www.shopliftingprevention.org). A random sample of 40 U.S. retailers were questioned concerning the disposition of the most recent shoplifter they apprehended. A total of 24 were turned over to police. Do these data provide sufficient evidence to contradict the NASP?
a. Describe a Type II error in terms of this application.
b. Calculate the probability β of a Type II error for this test, assuming that the true fraction of shoplifters turned over to the police is p = .55.
c. Suppose the number of retailers sampled is increased from 40 to 100. How does this affect the probability of a Type II error for p = .55?