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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

=+12. For each of the following scenarios, state whether a Type I, a Type II, or neither error has been made.
=+d) A pharmaceutical company tests whether a drug lifts the headache relief rate from the 25% achieved by the placebo.They fail to reject the null hypothesis because the P-value is 0.465. Further testing shows that the drug actually relieves headaches in 38% of people.
=+c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the
=+b) A student tests 100 students to determine whether other students on her campus prefer Coke or Pepsi and finds no evidence that preference for Coke is not 0.5. Later, a marketing company tests all students on campus and finds no difference.
=+a) A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers.They test H0: p = 0.3 vs. HA: p 7 0.3 and reject the null hypothesis. Later they find out that actually 28% of all customers enrolled.
=+11. For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly.
=+c) Construct a 95% confidence interval for m.
=+b) What is the critical value of t* for a 95% confidence interval?
=+10. Suppose that you are testing the hypotheses H0: m = 80 vs. HA: m ≠ 80. A sample of size 61 results in a sample mean of 75 and a standard deviation of 1.5.
=+d) Based on the confidence interval, at a = 0.05 can you reject H0? Explain.
=+c) Construct a 90% confidence interval for m.
=+b) What is the critical value of t* for a 90% confidence interval?
=+a) What is the standard error of the mean?
=+9. Suppose that you are testing the hypotheses H0: m = 16 vs. HA: m 6 16. A sample of size 25 results in a sample mean of 16.5 and a standard deviation of 2.0.
=+d) Which is used in computing the confidence interval?
=+a) The champion’s times are 56.3, 65.9, 50.5, 52.4, 46.5, 57.8, 52.2, and 43.2 seconds to complete the test course.Should they market the wax? Explain.
=+a) Construct a 90% confidence interval for p.b) Based on the confidence interval, at a = .05 can you reject H0? Explain.
=+8. Suppose that you are testing the hypotheses H0:p = 0.40 vs. HA: p 7 0.40. A sample of size 200 results in a sample proportion of 0.55.
=+d) Indicate which is used to calculate the confidence interval.
=+b) Based on the confidence interval, at a = 0.05 can you reject H0? Comment.
=+7. Suppose you are testing the hypotheses H0: p = 0.30 vs.HA: p ≠ 0.30. A sample size of 350 results in a sample proportion of 0.27.a) Construct a 95% confidence interval for p.
=+6. For each of the following situations, find the critical value for z or t.a) H0: m = 105 vs. HA: m ≠ 105 at a = 0.05; n = 61.b) H0: p = 0.05 vs. HA: p 7 0.05 at a = 0.05.c) H0: p = 0.6 vs. HA: p ≠ 0.6 at a = 0.01.d) H0: p = 0.5 vs. HA: p 6 0.5 at a = 0.01; n = 500.e) H0: p = 0.2 vs. HA: p 6
=+5. For each of the following situations, find the critical value(s) for z or t.a) H0: p = 0.3 vs. HA: p ≠ 0.3 at a = 0.05.b) H0: p = 0.5 vs. HA: p 7 0.5 at a = 0.05.c) H0: m = 12 vs. HA: m ≠ 12 at a = 0.05; n = 35d) H0: p = 0.4 vs. HA: p 7 0.4 at a = 0.01; n = 245e) H0: m = 20 vs. HA: m 6 20
=+d) If the P-value is 0.01, we reject the null hypothesis for any alpha level greater than 0.01.Section 12.3
=+b) If we use an alpha level of 0.01, then a P-value of 0.001 is statistically significant.c) If we use an alpha level of 0.01, then we reject the null hypothesis if the P-value is 0.001.
=+4. Which of the following statements are true? If false, explain briefly.a) It is better to use an alpha level of 0.05 than an alpha level of 0.01.
=+d) Using an alpha level of 0.05, a P-value of 0.06 means the null hypothesis is true.
=+b) Suppose they decide not to market the wax after the test, but it turns out that the wax really does lower the champion’s average time to less than 55 seconds. What kind of error have they made? Explain the impact to the company of such an error.
=+c) With an alpha level of 0.01, a P-value of 0.10 results in rejecting the null hypothesis.
=+b) The alpha level depends on the sample size.Exercises M12_SHAR8696_03_SE_C12.indd 415 14/07/14 7:30 AM 416 CHAPTER 12 More about Tests and Intervals
=+3. Which of the following statements are true? If false, explain briefly.a) Using an alpha level of 0.05, a P-value of 0.04 results in rejecting the null hypothesis.
=+d) A P-value of 0.90 is strong evidence that the null hypothesis is true.Section 12.2
=+2. Which of the following are true? If false, explain briefly.a) If the null hypothesis is true, you’ll get a high P-value.b) If the null hypothesis is true, a P-value of 0.01 will occur about 1% of the time.c) A P-value of 0.90 means that the null hypothesis has a good chance of being true.
=+a) A P-value of 0.01 means that the null hypothesis is false.b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.c) A P-value of 0.01 is evidence against the null hypothesis.d) A P-value of 0.01 means we should definitely reject the null hypothesis.
=+1. Which of the following are true? If false, explain briefly.
=+Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+Suppose that a year later, a full accounting of all the transactions at SmartWool (see page 404) finds that 26.5% of visits resulted in sales with an average purchase amount of $26.25. Have any errors been made?
=+8 Recall the mileage program test market of Question 4. Suppose after completing the hotel partnership, the mean revenue per customer is $40.26. Has a Type I or Type II error been made? Explain.
=+7 If the DVD strategy really works well—actually getting 60%of the people to pay off their balances—would the power of the test be higher or lower compared to a 32% payoff rate?Explain briefly.
=+what would the consequences be?
=+6 What’s a Type II error in the bank experiment context and
=+Explain what a Type I error is in this context and what the consequences would be to the bank.
=+5 Remember our bank that’s sending out DVDs to try to get customers to make payments on delinquent loans? It is looking for evidence that the costlier DVD strategy produces a higher success rate than the letters it has been sending.
=+vWhat does that say about the viability of the new arrangement?
=+4 The mileage rewards program at a major airline company has just completed a test market of a new arrangement with a hotel partner to try to increase engagement of valued customers with the program. The cost to the rewards program of the hotel offer is $35.00 per customer. From the test market,
=+52. Popcorn. Pop’s Popcorn, Inc. needs to determine the optimum power and time settings for their new licoriceflavored microwave popcorn. They want to find a combination of power and time that delivers high-quality popcorn with less than 10% of the kernels left unpopped, on average—a value
=+3 Given the confidence interval the bank found in the trial of the DVD mailing, what would you recommend be done?Should the bank scrap the DVD strategy?
=+2 The bank sets up an experiment to test the effectiveness of the DVD. The DVD is mailed to several randomly selected delinquent customers, and employees keep track of how many customers then contact the bank to arrange payments. The bank just got back the results on their test of the DVD
=+1 A bank is testing a new method for getting delinquent customers to pay their past-due credit card bills. The standard way was to send a letter (costing about $0.60 each) asking the customer to pay. That worked 30% of the time. The bank wants to test a new method that involves sending a DVD to
=+The analyst at SmartWool (see page 404) finds that the z-value for the sample proportion is 3.182 and the t-value for the sample mean amount sold is 0.896. Using a = 0.05, show that the same decisions would have been made using critical values
=+Suppose that an analyst at SmartWool wanted to test if the proportion of visits resulting in a sale from the new website has changed from the 0.20 it was historically. Suppose she also wants to know if the mean sale has increased from the average $24.85 that it was with the old site. To do that
=+Why did the researchers in the ADOPT study not express alarm about the increased risk they had seen?
=+Has helmet use in Florida declined among riders under the age of 21 subsequent to the change in the helmet laws
=+) If, in fact, the setting results in more than 10% kernels unpopped, what kind of error have they made? What will the consequence be for the company?
=+) To reduce the risk of making an error, the president (Pop himself) tells them to test 8 more bags of popcorn (selected at random) at the specified setting. They find the following percentage of unpopped kernels: 7, 13.2, 10, 6, 7.8, 2.8, 2.2,
=+5.2. Does this provide evidence that the setting meets their goal of less than than 10% unpopped? Explain.
=+d) Explain carefully what your P-value means in this context.
=+c) Should the company renew the contract? Support your recommendation with an appropriate test.
=+b) The station plans to conduct this test using a 10% level of significance, but the company wants the significance level lowered to 5%. Why?
=+a) What are the hypotheses?
=+. Radio ads. A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company’s product.The company contacts 600 people selected at random, and 133 can
=+) Explain what your P-value means in this context.
=+c) Should the professor spend the money for this software?Support your recommendation with an appropriate test.
=+b) Write the null and alternative hypotheses.
=+a) Is this a one-tailed or two-tailed test? Explain.
=+the dropout rate. The software is expensive, and the salesperson offers to let the professor use it for a semester to see if the dropout rate goes down significantly. The professor will have to pay for the software only if he chooses to continue using it. Initially, 203 students signed up for
=+45. Statistics software. A Statistics professor has observed that for several years about 13% of the students who initially enroll in his Introductory Statistics course withdraw before the end of the semester. A salesperson suggests that he try a statistics software package that gets students
=+c) Explain your conclusion.
=+b) Is there evidence that the proportion has decreased?
=+a) Find the z-score of the observed proportion.
=+44. India’s perspectives, part 2. In the same 2013–2014 survey conducted in Exercise 43, Pew Research reported that 62% of the respondents, from the sample of 2464, expect the economy to improve in the next 12 month. Two years before, in 2011, this percentage had been 60%. Is there evidence
=+c) Explain your conclusion.
=+b) Is there evidence that the proportion has changed?
=+a) Find the z-score of the observed proportion.
=+43. India’s perspectives. In its election year of 2014, India attracts strong media attention. In a Pew Research sample of 2464 adults, based on face-to-face interviews in Dec 2013 and Jan 2014, 57% of respondents judged the current state of the economy to be good. In 2012, that percentage was
=+42. Stocks. A young investor believes that he can beat the market by picking stocks that will increase in value. Assume that on average 50% of the stocks selected by a portfolio manager will increase over 12 months. Of the 25 stocks that the young investor bought over the last 12 months, 14 have
=+41. Business ethics. One study reports that 30% of newly hired MBAs are confronted with unethical business practices during their first year of employment. One business school dean wondered if her MBA graduates had similar experiences. She surveyed recent graduates from her school’s MBA
=+equipment. The day after the game, a pollster contacts 420 randomly chosen adults and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowl? Explain.
=+40. TV ads. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads.The goal of the company is that over 40% of the public recognize its brand
=+39. Living with parents. According to the UK Office for National Statistics, there has been, in the last two decades, a large increase in young adults (20-34 years old) living with their parents. In 2013, that percentage climbed to 26%. A municipality in South of England strives to do better by
=+38. Jury. Census data for a certain county shows that 19%of the adult residents are of Pacific ethnicity. Suppose 72 people are called for jury duty, and only 9 are Pacific. Does this apparent underrepresentation call into question the fairness of the jury selection system? Explain.
=+37. Women executives. A company is criticized because only 13 of 43 people in executive-level positions are women.The company explains that although this proportion is lower than it might wish, it’s not surprising given that only 40% of their employees are women. What do you think?Test an
=+test. Although the packet claims a germination rate of 92%, only 171 of 200 test seeds sprout. Is this evidence that the seeds have lost viability during a year in storage? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied
=+36. Truth in advertising. A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The manager finds a packet of last year’s green bean seeds and plants them as a
=+35. WebZine. A magazine called WebZine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacts a simple random sample of 500 current subscribers, and 137 of those surveyed
=+the company must sell those machines at drastically reduced prices. The company goal is to keep the proportion of damaged machines below 2%. One day an inspector randomly checks 60 washers and finds that 5 of them have scratches or dents. Is this strong evidence that the warehouse is failing
=+34. Damaged goods. An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor,
=+33. Maintenance costs. A limousine company is concerned with increasing costs of maintaining their fleet of 150 cars.After testing, the company found that the emissions systems of 7 out of the 22 cars they tested failed to meet pollution control guidelines. They had forecasted costs assuming that
=+a) Create a 90% confidence interval for the true level of dissatisfaction among customers.b) Test an appropriate hypothesis and state your conclusion.
=+32. Customer satisfaction. A company hopes to improve customer satisfaction, setting as a goal no more than 5%negative comments. A random survey of 350 customers found only 10 with complaints.
=+a) Create a 95% confidence interval for the proportion of workers who have invested in individual retirement accounts based on the survey.b) Test an appropriate hypothesis and state your conclusion.
=+31. Retirement. A survey of 1000 workers indicated that approximately 520 have invested in an individual retirement account. National data suggests that 44% of workers invest in individual retirement accounts.
=+e) Do you think this difference is meaningful? Explain.
=+a) Write appropriate hypotheses.b) Check the assumptions and conditions.c) Perform the test and find the P-value.d) State your conclusion.
=+answered affirmative to the question: Is climate change happening? In the fourth version in 2013, the figure increased to 81%, with a random sample of 5219 adults. Is this a significant increase?
=+30. Global warming, part 2. Although meant to be annual, CSIRO repeated their survey in September 2011, and found, in this second survey, that 77% of Australian citizens
=+c) Perform the test and find the P-value.d) State your conclusion.e) Do you think this difference is meaningful? Explain.
=+: “Is climate change happening?” which is quite a high percentage when compared internationally. In the fourth version in 2013, the figure however declined to 81%, with a random sample of 5219 adults. Is this a significant decline?a) Write appropriate hypotheses.b) Check the assumptions and

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