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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

=+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
=+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
=+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
=+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
=+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:
=+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
=+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
=+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%
=+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
=+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
=+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
=+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
=+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
=+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
=+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
=+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
=+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
=+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
=+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
=+) 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
=+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
=+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
=+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,
=+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
=+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
=+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
=+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
=+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.
=+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
=+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,
=+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
=+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
=+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 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
=+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
=+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
=+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
=+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

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