Shoplifting costs retail businesses a great deal of money every year. In spite of this the historical evidence suggests that only 50% of all shoplifters are turned over to the police. A random survey of 40 retailers revealed that 24 of them had turned their most recent shoplifter in to the police. Use alpha = 0.05 for all tests.
a. Test to see if this sample data indicates that more shoplifters are being turned in than in the past?
b. What assumptions must hold for this test to be performed?
c. Find the p-value for part a. (It is the probability that z is greater than the absolute value of the test statistic in part a.)
d. Describe both Type I and Type II errors in the context of this problem.
e. Calculate the probability of Type II error if the true proportion of shoplifters turned over to police is 55%.
f. Calculate the probability of Type II error if the true proportion of shoplifters turned over to police is 55% , if the sample size is increased to 100.
g. What does this tell you about the relationship between alpha, beta and sample size?