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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

Suppose a random sample of 100 observations from a binomial population gives a value of \(\hat p = .63\) and you wish to test the null hypothesis that the population parameter p is equal to .70 against the alternative hypothesis that p is less than .70.

a. Noting that\(\hat p = .63\) what does your intuition tell you? Does the value of \(\hat p\) appear to contradict the null hypothesis?

Solder-joint inspections. Current technology uses high-resolution X-rays and lasers to inspect solder-joint defects on printed circuit boards (PCBs) (Global SMT & Packaging, April 2008). A particular manufacturer of laser-based inspection equipment claims that its product can inspect, on average, at least 10 solder joints per second when the joints are spaced .1 inch apart. The equipment was tested by a potential buyer on 48 different PCBs. In each case, the equipment was operated for exactly 1 second. The number of solder joints inspected on each run follows:

The potential buyer wants to know whether the sample data refute the manufacturer鈥檚 claim. Specify the null and alternative hypotheses that the buyer should test.

Intrusion detection systems. The Journal of Research of the National Institute of Standards and Technology (November鈥� December 2003) published a study of a computer intrusion detection system (IDS). The IDS is designed to provide an alarm whenever unauthorized access (e.g., an intrusion) to a computer system occurs. The probability of the system giving a false alarm (i.e., providing a warning when no intrusion occurs) is defined by the symbol 伪, while the probability of a missed detection (i.e., no warning given when an intrusion occurs) is defined by the symbol 尾. These symbols are used to represent Type I and Type II error rates, respectively, in a hypothesis-testing scenario

a. What is the null hypothesis, H0?

b. What is the alternative hypothesis,Ha?

c. According to actual data collected by the Massachusetts Institute of Technology Lincoln Laboratory, only 1 in 1,000 computer sessions with no intrusions resulted in a false alarm. For the same system, the laboratory found that only 500 of 1,000 intrusions were actually detected. Use this information to estimate the values of 伪and 尾.

Which of the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test

The National Association of Realtors (NAR) reported the results of an April 2015 survey of home buyers. In a random sample of 1,971 residential properties purchased during the year, 414 were purchased as a vacation home. Five years ago, 10% of residential properties were vacation homes.

a. Do the survey results allow the NAR to conclude (at 伪=.01) that the percentage of all residential properties purchased for vacation homes is greater than 10%?

b. In a previous year, the NAR sent the survey questionnaire to a nationwide sample of 45,000 new home owners, of which 1,982 responded to the survey. How might this bias the results? [Note: In the most recent survey, the NAR used a more valid sampling method.
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