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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
=+29. Global warming. In CSIRO’s first ‘Annual survey of Australian attitudes to climate change’ in 2011, no less than 82.2% of Australian citizens answered yes to the M10_SHAR8696_03_SE_C10.indd 355 14/07/14 7:31 AM 356 CHAPTER 10 Testing Hypotheses about Proportions
=+d) State your conclusion.e) Do you think this difference is meaningful? Explain.
=+) Write appropriate hypotheses.b) Check the assumptions and conditions.c) Perform the test and find the P-value.
=+. Billing company. A billing company that collects bills for doctors’ offices in the area is concerned that the percentage of bills being paid by Medicare has risen. Historically, that percentage has been 31%. An examination of 8368 recent bills reveals that 32% of these bills are being paid
=+f) Do chemicals in the environment cause congenital abnormalities?
=+e) What’s your conclusion?
=+) Explain carefully what the P-value means in this context.
=+c) Perform the mechanics of the test. What is the P-value?
=+a) Write appropriate hypotheses.b) Check the necessary assumptions.
=+27. Environment. In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study
=+Do these responses provide strong evidence that more than half of adults are thriving? Correct the mistakes you find in the following student’s attempt to test an appropriate hypothesis.H0: pn = 0.5 HA: pn 7 0.5 SRS, 1000 7 10 530 1000 = 0.530; SD1pn2 = B 10.53210.472 1000 = 0.016 Since the
=+26. Gallup Poll, part 2. The Gallup-Healthways WellBeing Index tracks daily how Americans evaluate their lives, both now and in five years, on the Cantril SelfAnchoring Striving Scale, where “0” represents the worst possible life and “10” represents the best possible life.Respondents
=+There is strong evidence that the new system does not work.
=+25. Product testing. Since many people have trouble using all of the features on their smart phones, an executive training company has developed what it hopes will be easier instructions. The goal is to have at least 96% of customers succeed at being able to use any feature they wish. The
=+cardinal Jorge Mario Bergoglio as the new Pope in March 2013 had a major impact on the Vatican’s perception in global news. In the period March 2012 – March 2013, under Francis’ predecessor Pope Benedict, 30% of twitter conversations had a positive tone and 70% had a negative tone. Between
=+24. Pope Francis media coverage. The election of Argentine
=+b) Find a 95% confidence interval for the South Korean sample.
=+) Is the South Korean percentage different from that worldwide? Test the appropriate hypothesis. Check conditions. Does the test provide evidence that the percentage indeed differs?
=+. Financial instability. The Pew Research Center’s Global Attitudes Project refers to ‘top global threats’ according to the public in 39 countries. Financial instability is regarded as one of the two major global threats, but to different degrees. According to the 2013 survey, while 52% of
=+d) How many times in a row would you have to get the coffee coupon instead of cash savings to be pretty sure that the company isn’t living up to its advertised percentage of winners? Justify your answer by calculating a probability and explaining what it means.
=+c) Would three losses in a row convince you that the store is cheating?M10_SHAR8696_03_SE_C10.indd 354 14/07/14 7:31 AM Exercises 355
=+b) You try a third time. You get coffee again! What’s the probability of not getting a cash savings three times in a row if half the cards really do offer cash savings?
=+) The first time you shop there, you get the coffee coupon.You try again and again get the coffee coupon. Do two failures in a row convince you that the true fraction of winners isn’t 50%? Explain.
=+22. Scratch off. A retail company offers a “scratch off” promotion. Upon entering the store, you are given a card.When you pay, you may scratch off the coating. The company advertises that half the cards are winners and have immediate cash-back savings of $5 (the others offer $1 off any
=+b) Do you think that half of the M&M’s® candies in the bag are really red? Explain.
=+21. False claims? A candy company claims that in a large bag of holiday M&M’s® half the candies are red and half the candies are green. You pick candies at random from a bag and discover that of the first 20 you eat, 12 are red.a) If it were true that half are red and half are green, what is
=+20. Car sales. A German automobile company is counting on selling more cars to the younger market segment—drivers under the age of 20. The company’s market researchers survey to investigate whether or not the proportion of today’s high school seniors who own their own cars is higher than
=+. Product effectiveness. A pharmaceutical company’s old antacid formula provided relief for 70% of the people who used it. The company tests a new formula to see if it is better and gets a P-value of 0.27. Is it reasonable to conclude that the new formula and the old one are equally
=+d) There’s a 3% chance that a random sample could produce the results we observed if p = .7, so it’s reasonable to conclude that the fund manager is not correct.e) There’s a 3% chance that the null hypothesis is correct.
=+a) There’s a 3% chance that the fund manager is correct.b) There’s a 97% chance that the fund manager is correct.c) There’s a 3% chance that a random sample could produce the results we observed, so it’s reasonable to conclude that the fund manager is correct.
=+18. Mutual funds. A mutual fund manager claims that at least 70% of the stocks she selects will increase in price over the next year. We examined a sample of 200 of her selections over the past three years. Our P-value turns out to be 0.03.Which conclusion is appropriate? Explain.
=+hires a consultant to help her. The consultant selects a random sample of recent purchases, tests the hypothesis that the ads produced no change against the alternative that the percent who use the one-click feature is now greater than 10%, and finds a P-value of 0.22. Which conclusion is
=+17. Ad campaign. An information technology analyst believes that they are losing customers on their website who find the checkout and purchase system too complicated.She adds a one-click feature to the website, to make it easier but finds that only about 10% of the customers are using it. She
=+16. Another P-value. A company developing a new digital camera for spotting speeding offenders on major highway systems has concluded that the new device is significantly better than the current camera system. The company made this decision based on a P-value of 0.04. Explain the meaning of the
=+15. P-value. Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic have failed to find evidence of a significant change compared with three years ago. Explain what the study’s P-value of 0.17 means in this context.
=+d) There’s a 96.6% chance that 50% of the houses take more than three months to sell.
=+c) There’s a 3.4% chance that the null hypothesis is correct.
=+b) If 50% of the houses take more than three months to sell, there’s a 3.4% chance that a random sample would produce a sample proportion as high as the one they obtained.
=+a) There’s a 3.4% chance that 50% of the houses take more than three months to sell.
=+. House sales. The realty company in Exercise 11b looks at a recent sample of houses that have sold. On testing the null hypothesis that 50% of the houses take more than three months to sell against the hypothesis that more than 50% of the houses take more than three months to sell, they find a
=+d) There’s a 22% chance that natural sampling variation could produce a sample with an observed proportion of on-time deliveries such as the one they obtained if, in fact, 90% of deliveries are on time.
=+13. Deliveries. The clothing company in Exercise 11a looks at a sample of delivery reports. They test the hypothesis that 90% of the deliveries are on time against the alternative that greater than 90% are on time and find a P-value of 0.22. Which of these conclusions is appropriate?a) There’s
=+c) A market researcher for a cola company decides to field test a new soft drink flavor, planning to market it only if he is sure that over 60% of the people like the flavor.
=+b) Recently, 20% of cars of a certain model have needed costly transmission work after being driven between 50,000 and 100,000 miles. The car manufacturer hopes that the redesign of a transmission component has solved this problem.
=+a) A 2010 Harvard Business Review article looked at 1109 CEOs from global companies and found that 32% had MBAs. Has the percentage changed?
=+12. More hypotheses. Write the null and alternative hypotheses to test each of the following situations.
=+11. Hypotheses. Write the null and alternative hypotheses to test each of the following situations.a) An online clothing company is concerned about the timeliness of their deliveries. The VP of Operations and Marketing recently stated that she wanted the percentage of products delivered on time
=+b) If the test yields a high P-value and the researcher fails to reject the null hypothesis, but the new drug is more effective, what are the consequences of such a mistake?Chapter Exercises
=+a) If the test yields a low P-value and the researcher rejects the null hypothesis, but it actually is not better, what are the consequences of such a mistake?
=+. Developing a new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct a clinical trial to compare the effectiveness to the most widely used current treatment. The results will be
=+b) If the test yields a high P-value and the researcher fails to reject the null hypothesis, but there is a bad side effect of the drug, what are the consequences of such a mistake?
=+a) If the test yields a low P-value and the researcher rejects the null hypothesis, but there is actually no ill side effect of the drug, what are the consequences of such a mistake?
=+9. Occasionally, a report comes out that a drug that cures some disease turns out to have a nasty side effect. For example, some antidepressant drugs may cause suicidal thoughts in younger patients. A researcher wants to study such a drug and look for evidence that such side effects exist.
=+c) A student wants to know if other students on her campus prefer Coke or Pepsi.Section 10.6
=+b) The last time a philanthropic agency requested donations, 4.75% of people responded. From a recent pilot mailing, they wonder if that rate has increased.
=+a) Consumer Reports discovered that 20% of a certain computer model had warranty problems over the first three months. From a random sample, the manufacturer wants to know if a new model has improved that rate.
=+8. For each of the following, write out null and the alternative hypotheses, being sure to indicate whether the alternative is one-sided or two-sided.
=+c) A presidential candidate for a student union wants to know, using an internet survey on the campus website, whether he will win the elections or not.
=+b) Last year, 56% of university professors enrolled in at least one membership at the local hotel and spa. A survey is conducted to check whether the current members will renew their membership for the next year.
=+a) An airline company reports that last year 85% of their flights arrived on time. From a random sample this year, they want to know if that proportion has changed.
=+. For each of the following scenarios, write out the null and alternative hypotheses, being sure to state whether the alternative is one sided or two sided.
=+) Does the z-statistic seem like a particularly large or small value?Section 10.5
=+b) Find the z-statistic.
=+) Find the standard deviation of the sample proportion based on the null hypothesis.
=+6. A survey of 200 university professors finds that 120 think that the level of education will improve in the next 10 years. Is there evidence that the rate is higher among all professors than 50% reported by the public at large?
=+c) Does the z-statistic seem like a particularly large or small value?
=+b) Find the z-statistic.
=+a) Find the standard deviation of the sample proportion based on the null hypothesis.
=+5. A consulting firm had predicted that 35% of the employees at a large firm would take advantage of a new company Credit Union, but management is skeptical. They doubt the rate is that high. A survey of 300 employees shows that 138 of them are currently taking advantage of the Credit Union.
=+c) A P-value above 0.10 shows that the null hypothesis is true.d) If the null hypothesis is true, you can’t get a P-value below 0.01.Section 10.4
=+b) A high P-value is strong evidence in favor of the null hypothesis.
=+a) A very low P-value provides evidence against the null hypothesis.
=+4. Which of the following are true? If false, explain briefly.
=+d) A P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.
=+b) A very low P-value proves that the null hypothesis is false.c) A high P-value shows that the null hypothesis is true.
=+3. Which of the following are true? If false, explain briefly.a) A very high P-value is strong evidence that the null hypothesis is false.
=+c) Regular card customers have a default rate of 6.7%. A credit card bank wants to know if that rate is different for their Gold card customers.Section 10.3
=+b) Last year, a survey found that 45% of the employees were willing to pay for on-site day care. The company wants to know if that has changed.
=+a) A recent UMass-Amherst study found that seat-belt compliance in Massachusetts was 73% in 2011. The state wants to know if it has changed.
=+2. As in Exercise 1, for each of the following situations, write the null and alternative hypotheses in terms of parameter values.
=+c) A bank wants to know if the percentage of customers using their website has changed from the 40% that used it before their system crashed last week.
=+b) A pharmaceutical company wonders if their new drug has a cure rate different from the 30% reported by the placebo.
=+) A casino wants to know if their slot machine really delivers the 1 in 100 win rate that it claims.
=+. For each of the following situations, write the null and alternative hypotheses in terms of parameter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5.
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+What are the undesirable consequences?
=+Identify the ethical dilemma in this scenario.
=+who find pain relief using their new product Z-170 was 0.06.Should he conclude that the product doesn’t work?
=+A marketing analyst at a biotechnology firm has just learned that the P-value for testing whether the proportion of people
=+An accountant at an organic food chain is testing whether the customers prefer a new cheese supplier. She surveys 100 customers and finds out that the proportion preferring the new supplier is greater than the previous proportion with a P-value of 0.002. The new supplier costs more, but the
=+What should we conclude about the new design of the website from page 336?
=+What’s the P-value associated with a one-proportion z-test of our null hypothesis?
=+Question Are the conditions for inference satisfied?
=+3 The new allergy drug is tested, and the P-value is 0.0001. What would you conclude about the new drug?
=+2 An allergy drug has been tested and found to give relief to 75% of the patients in a large clinical trial. Now the scientists want to see whether a new, “improved”version works even better. What would the null hypothesis be?
=+aspirin doesn’t work. What would you say?
=+1 A pharmaceutical firm wants to know whether aspirin helps to thin blood. The null hypothesis says that it doesn’t. The firm’s researchers test 12 patients, observe the proportion with thinner blood, and get a P-value of 0.32. They proclaim that
=+the new site? What are the right hypotheses for a test?
=+Does this suggest that the click-through proportion has changed with
=+Does this suggest that the click-through proportion has changed with the new site? What are the right hypotheses for a test?
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