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Chapter 7: Q1E (page 397)
Which hypothesis, the null or the alternative, is the status-quo hypothesis? Which is the research hypothesis?
The null hypothesis is a statement that represents the status-quo hypothesis.
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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?
Accidents at construction sites. In a study published in the Business & Economics Research Journal (April 2015), occupational accidents at three construction sites in Turkey were monitored. The total numbers of accidents at the three randomly selected sites were 51, 104, and 37.
Summary statistics for these three sites are:\(\bar x = 64\)and s = 35.3. Suppose an occupational safety inspector claims that the average number of occupational accidents at all Turkish construction sites is less than 70
a. Set up the null and alternative hypotheses for the test.
b. Find the rejection region for the test using\(\alpha = .01\)
c. Compute the test statistic.
d. Give the appropriate conclusion for the test.
e. What conditions are required for the test results to be valid?
For the binomial sample sizes and null hypothesized values of p in each part, determine whether the sample size is large enough to use the normal approximation methodology presented in this section to conduct a test of the null hypothesis \({H_0}:p = {p_0}\)
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’s claim. Specify the null and alternative hypotheses that the buyer should test.
Student loan default rate. The national student loan default rate has fluctuated over the past several years. Recently (October 2015) the Department of Education reported the default rate (i.e., the proportion of college students who default on their loans) at 0.12. Set up the null and alternative hypotheses if you want to determine if the student loan default rate this year is less than 0.12.
The testing claimed by the national student loan default rate is the test for a specified proportion.
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