# Probability Assignment | Professional Writing Services

• (24) 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 over to the police.  Use alpha = 0.05 for all tests.

1.(6)  Test to see if this sample data indicates that more shoplifters are being turned in than in the past?

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2.(2)  What assumptions must hold for this test to be performed?

3.(2)  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.)

4.(2) Describe both Type I and Type II errors in the context of this problem.

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5.(5) Calculate the probability of Type II error if the true proportion of shoplifters turned over to police now is 55%.

6.(5) Calculate the probability of Type II error if the true proportion of shoplifters turned over to police now is 55%, if the sample size is increased to 100.

7.(2) What does this tell you about the relationship between alpha, beta and sample size?

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