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Chapter 7: Q134SE (page 444)

Arresting shoplifters. 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. Conduct a hypothesis test to answer the question of interest. Use\(\alpha = 0.05\).

b. Is the sample size large enough to use the inferential procedure of part a?

c. Find the observed significance level of the hypothesis test in part a. Interpret the value.

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

Short Answer

Expert verified

The null and the alternative hypotheses are\({H_0}:P = 0.50\)and\({H_a}:P > 0.50\)

Step by step solution

01

Given information

The information is regarding the National Association of Shoplifting Prevention (NASP) U.S retailers.

Random samples of 40 U.S retailers were questioned concerning the deposition of the most recent shoplifter they apprehended.

A total of 24 were turned over to police. Here NASP claims that only 50% of all shoplifting are turned over to police.

From the above information,

\(\begin{aligned}{p_0} &=0.50\\{q_0} &= 1 - {p_0}\\ &= 0.50\end{aligned}\)

02

Concept of the null and the alternative hypothesis

The null hypothesis of a test always predicts no effect or no association between variables, while the alternative hypothesis states your research's prediction of an effect or relationship.

03

Setting up the null and the alternative hypothesis

a.

From this information,

Null hypothesis:

\({H_0}:P = 0.50\)

Only 50% of U.S. retailers are shoplifting is turned over to police

Alternative hypothesis:

\({H_a}:P > 0.50\)

Not only 50% of U.S. retailers are shoplifting is turned over to police.

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Most popular questions from this chapter

Question:Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting (January 2008) study of Machiavellian traits in accountants, Exercise 6.19 (p. 341). A Mach rating score was determined for each in a random sample of 122 purchasing managers, with the following results:x̄ = 99.6 s = 12.6. Recall that a director of purchasing at a major firm claims that the true mean Mach rating score of all purchasing managers is 85.

a. Suppose you want to test the director’s claim. Specify the null and alternative hypotheses for the test.

b. Give the rejection region for the test using α = 0.10.

c. Find the value of the test statistic.

d. Use the result, part c, to make the appropriate conclusion.

Hotels’ use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelers’ familiarity with ecolabels used by hotels, Exercise 2.64 (p. 104). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, “Suppose the response is measured on a continuous scale from 10 (not familiar at all) to 50 (very familiar).” The mean and standard deviation for the Energy Star ecolabel are 44 and 1.5, respectively. Assume the distribution of the responses is approximately normally distributed.

a. Find the probability that a response to Energy Star exceeds 43.

b. Find the probability that a response to Energy Star falls between 42 and 45. c. If you observe a response of 35 to an ecolabel, do you think it is likely that the ecolabel was Energy Star? Explain.

A simple random sample of 25 observations was selected from a normal population. The mean and standard deviation of this sample are 20 and 5, respectively.

a. Test H0:μ=22against Ha:μ≠22at the 10% significance level.

b. Test H0:μ≥22against H0:μ≤22at the 1% significance level.

In a test of H0:μ=100againstHa:μ>100, the sample data yielded the test statistic z = 2.17. Find and interpret the p-value for the test.

In a test of \({H_0}:\mu = 100\) against \({H_a}:\mu \ne 100\), the sample data yielded the test statistic z = 2.17. Find the p-value for the test.
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