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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+d) Will the power be greater if the repair shop’s inspectors are only a little out of compliance or a lot? Why?
=+c) Will the power be greater if they use a 5% or a 10%level of significance? Why?
=+) Will the power be greater if they test 20 or 40 cars?Why?
=+35. Cars, again. As in Exercise 33, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards.
=+d) Which type of error might customers consider more serious?
=+b) Explain in this context what happens if the quality control people commit a Type I error.
=+c) Which type of error would the factory owner consider more serious?
=+34. Quality control. Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be
=+d) Which type of error might environmentalists consider more serious?
=+c) Which type of error would the shop’s owner consider more serious?
=+c) Explain in this context what happens if the quality control people commit a Type II error.
=+b) In this context, what is a Type II error?
=+33. Testing cars. A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect
=+e) What is the power of this test?
=+d) Which is worse here, a Type I or Type II error? Explain.
=+c) What would a Type II error mean?
=+45. TV safety, revisited. The manufacturer of the metal TV stands in Exercise 43 is thinking of revising its safety test.
=+b) What would a Type I error mean?
=+) Put this in the context of a hypothesis test. What are the null and alternative hypotheses?
=+. Prostate Cancer. Prostate cancer is the most common cancer found in men. Physicians routinely perform a Prostate-Specific Antigen (PSA) test to determine whether there is any evidence of prostate cancer. A patient who tested positive would then go then through an expensive biopsy that costs
=+) What would the power of the test represent in this context?
=+d) For each type of error, tell who would be harmed.
=+a) In words, what will their hypotheses be?b) What would a Type I error be?c) What would a Type II error be?
=+a) If the company’s lawyers are worried about being sued for selling an unsafe product, should they increase or decrease the value of a? Explain.
=+31. Homeowners. In 2012, the Gallup Poll reported that only 62% of American families owned their homes, the lowest percentage reported in a decade. Census data reveal that the ownership rate in one small city is even lower.The city council is debating a plan to offer tax breaks to first-time
=+b) What could you do to increase the filter’s power?
=+30. More spam. Consider again the points-based spam filter described in Exercise 28. When the points assigned to various components of an e-mail exceed the cutoff value you’ve set, the filter rejects its null hypothesis (that the message is real) and diverts that e-mail to a junk
=+c) What’s the disadvantage of doing that?
=+b) What could the bank do to increase the power?
=+b) In this context, what is meant by the power of the test?
=+a) In this context, what is meant by the power of the test?
=+29. Second loan. Exercise 27 describes the loan score method a bank uses to decide which applicants it will lend money. Only if the total points awarded for various aspects of an applicant’s financial condition fail to add up to a minimum cutoff score set by the bank will the loan be denied.
=+b) Which kind of error is it when a real message gets classified as junk?
=+a) When the filter allows spam to slip through into your inbox, which kind of error is that?
=+We can think of the filter’s decision as a hypothesis test. The null hypothesis is that the e-mail is a real message and should go to your inbox. A higher point total provides evidence that the message may be spam; when there’s sufficient evidence, the filter rejects the null, classifying
=+c) If the company wants to increase the power of the test, what options does it have? Explain the advantages and disadvantages of each option.M12_SHAR8696_03_SE_C12.indd 420 14/07/14 7:30 AM Exercises 421
=+28. Spam. Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message, and so on. The higher the point total, the
=+d) What impact does this change in the cutoff value have on the chance of each type of error?
=+c) Suppose the bank decides to lower the cutoff score from 250 points to 200. Is that analogous to choosing a higher or lower value of a for a hypothesis test? Explain.
=+b) Which kind of error is it when the bank misses an opportunity to make a loan to someone who would have repaid it?
=+a) When a person defaults on a loan, which type of error did the bank make?
=+can think of this decision as a hypothesis test. Since the bank makes its profit from the interest collected on repaid loans, their null hypothesis is that the applicant will repay the loan and therefore should get the money. Only if the person’s score falls below the minimum cutoff will the
=+27. Loans. Before lending someone money, banks must decide whether they believe the applicant will repay the loan.One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person’s income level, credit history, current debt
=+46. Catheters, again. The catheter company in Exercise 44 is reviewing its testing procedure.
=+a) Explain why she can reject the null hypothesis that p = 0.159 vs. p 6 0.159 at a = 0.05.
=+26. Computer skills again. The health care analyst in Exercise 18 finds a 90% confidence interval for the true proportion of employees who fail the course to be (14.46%, 15.74%).
=+b) Explain why the difference may or may not be important
=+25. Measles revisited. The analyst in Exercise 17 finds a 98% confidence interval for the true proportion of vaccinated children to be (0.9707, 0.9773).a) Explain why she can reject the null hypothesis that p = 0.98 vs. p 6 0.98 at a = 0.01.
=+a) Suppose the significance level is changed to a = 0.01.Will the probability of a Type II error increase, decrease, or remain the same?
=+c) Why did you probably not need to look up the critical value inb) to reach your conclusion?
=+b) Look up the 0.001 upper critical value for a z-statistic and state your conclusion about the test.
=+a) Explain what the z-statistic means in this context.
=+24. Web finder. Zocdoc.com provides a service to find and make appointments with medical professionals across the United States. Suppose an analyst looking to see if a new web design had improved the percentage of people successfully making appointments found a z-score of 10.23.
=+b) What is meant by the power of the test the company conducts?
=+c) Why did you probably not need to find the lower critical value inb) to reach your conclusion?
=+b) How many degrees of freedom are associated to the t-statistic? Find the 0.005 lower critical value for this t-statistic and state your conclusion about the delivery times.
=+a) Explain what the t-statistic means in this context.
=+23. Delivery time. A courier service manager is advertising that the average delivery time for his company is less than 10 hours for local deliveries. The manager records the delivery times for a random sample of 30 deliveries across town and gets a t-statistic of -20.
=+c) Suppose the manufacturing process is slipping out of proper adjustment. As the actual mean diameter of the catheters produced gets farther and farther above the desired 2.00 mm, will the power of the quality control test increase, decrease, or remain the same?
=+b) The result is statistically significant, but is it important?Comment.M12_SHAR8696_03_SE_C12.indd 417 14/07/14 7:30 AM 418 CHAPTER 12 More about Tests and Intervals
=+d) What could they do to improve the power of the test?
=+47. Two coins. In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%- or the
=+17. Measles. Health researchers at a large HMO base their cost predictions for measles on the belief that 98% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 97.4%had been
=+16. Alpha, again. Analysts evaluating a new program to encourage customer retention in a test market find no evidence of an increased rate of retention in a test of 2000 customers. They based this conclusion on a test using a = 0.01. Would they have made the same decision at a = 0.05? How about
=+15. Alpha. A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using a = 0.05. Would he have made the same decision at a = 0.10? How about a = 0.01?
=+a) What is the alternative hypothesis?
=+b) Given that the outcome of your spin is tails, what would you decide? What if it were heads?
=+a) If the test had been performed at a = .01, would the test have been more or less likely to reject the null hypothesis of no increase in the risk of heart attack?b) Which alpha level should be used? Why?Chapter Exercises
=+c) How large is a in this case?
=+22. Safety. A drug that reduces cholesterol level is suspected to increase the risk of heart attack, which could be dangerous. A test of the drug fails to reject the null hypothesis of no increase in the risk of heart attack when tested at a = .05.
=+d) How large is the power of this test? (Hint: How many possibilities are in the alternative hypothesis?)
=+e) How could you lower the probability of a Type I error and increase the power of the test at the same time?
=+b) If he chose the alpha level 7.2% so that he could claim statistical significance, explain why this is not an ethical use of statistics.
=+48. Faulty or not? You are in charge of shipping computers to customers. You learn that a faulty RAM chip was put into some of the machines. There’s a simple test you can perform, but it’s not perfect. All but 4% of the time, a good chip passes the test, but unfortunately, 35% of the bad
=+a) If instead he had used an alpha level of 5%, is it more or less likely that he would have rejected his null hypothesis? Explain.
=+a) What are the null and alternative hypotheses?
=+21. Convenient alpha. An enthusiastic junior executive has run a test of his new marketing program. He reports that it resulted in a “significant” increase in sales. A footnote on his report explains that he used an alpha level of 7.2% for his test. Presumably, he performed a hypothesis test
=+b) Given that a computer fails the test, what would you decide? What if it passes the test?
=+b) A pundit on a TV news show claimed that only 6% of working men had a second job. Use your confidence interval to test whether his claim is plausible given the poll data.
=+c) How large is a for this test?
=+d) What is the power of this test? (Hint: How many possibilities are in the alternative hypothesis?)
=+a) Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval.
=+20. Hard times. In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills. (www.careerbuilder.com)
=+49. Collections, part 2. The owner of the collection agency in Exercise 41 is quite certain that they can collect more than $200 per customer on average. He urges that the credit card company run a larger trial. Do you think a larger trial might help the company make a better decision? Explain.
=+c) What is the level of significance of this test? Explain.
=+b) A grocery store owner believed that at least 75% of women are the primary grocery shopper for their family, and targets his advertising accordingly. He wishes to conduct a hypothesis test to see if the fraction is in fact higher than 75%. What does your confidence interval indicate? Explain.
=+a) Estimate the percentage of all European females who identify themselves as the primary grocery shopper. Use a 95% confidence interval being sure to check the conditions.
=+19. Groceries. In April 2011, a survey was conducted on 2500 European women. 1950 of them identified themselves as the primary grocery shopper in their household.
=+50. Free gift, part 2. The philanthropic organization of Exercise 42 decided to go ahead with the new gift. In mailings to 98,000 prospects, the new mailing yielded an average of$0.78. If they had decided based on their initial trial not to use this gift, what kind of error would they have
=+) Even though this program has been shown to be significantly better statistically, why might you not recommend that your company adopt it?
=+a) Explain what the P-value means in this context.
=+%. The hypothesis that the program produced no improvement was rejected with a P-value of 0.023.
=+. Computer skills. A new program may reduce the proportion of employees who fail a computer skills course. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8500 employees in several different sites. Statistical analysis of
=+b) If she wants the power to be the same, but she is interested in detecting an increase of only 1 point, what will she need to do?
=+a) If the actual increase is only 1 point, will the power be increased or decreased?
=+13. Most car engines need at least 87 octane to avoid“knocking” or “pinging,” terms used to describe the preignition that can happen when a fuel’s octane is too low.An engineer is designing an experiment to raise the octane of an ethanol-based fuel. From previous studies, she thinks
=+d) A test of H0: p = 0.6 vs. HA: p 6 0.6 fails to reject the null hypothesis. Later it is discovered that p = 0.5 Section 12.6
=+b) A test of H0: p = 0.7 vs. HA: p 6 0.7 fails to rejects the null hypothesis. Later it is discovered that p = 0.8 M12_SHAR8696_03_SE_C12.indd 416 14/07/14 7:30 AM Exercises 417c) A test of H0: p = 0.4 vs HA: p ≠ 0.4 rejects the null hypothesis. Later it is discovered that p = 0.55
=+a) A test of H0: m = 20 vs. HA: m 7 20 rejects the null hypothesis. Later it is discovered that m = 19.9
=+51. Pricing for competitiveness. SLIX wax is developing a new high performance fluorocarbon wax for cross country ski racing designed to be used under a wide variety of conditions. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time to finish
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