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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
=+Are the results they find independent of the telephone type?
=+. To complete the poll reported in Exercise 9, Pew Research surveyed respondents by telephone, drawing a random sample of landlines and another random sample of cell phones. For those numbers that were valid, they report the following:Land Cell Total No Answer/Busy 552 42 594 Voicemail 3347
=+d) What do you conclude?
=+) How many degrees of freedom does it have?
=+b) Compute the x2 statistic.
=+a) Under the usual null hypothesis, what are the expected values?
=+. The same poll as in Exercise 9 has asked about social networking over several years and for different age groups.Here is a table of responses:May-2010 Aug-2011 Aug-2012 Total Age 18–29 273 277 293 843 30–49 325 362 388 1075 50–64 259 270 314 843 Total 857 909 995 2761
=+) Find a 95% confidence interval for the difference between these proportions.Section 14.6
=+) What is the standard error of the difference?
=+) What is the difference in proportions?
=+) Find the proportions of each income group who are social networking users.
=+. From the same survey as in Exercise 9, 294 of the 409 respondents who reported earning less than $30,000 per year said they were social networking users. At the other end of the income scale, 333 of the 504 respondents reporting earnings of $75,000 or more were social networking users.
=+d) Find a 95% confidence interval for the difference between the proportions.
=+c) What is the standard error of the difference?
=+) What is the difference in proportions?
=+a) Find the proportions of male and female Internet users who said they use social networking.
=+9. Markets have become interested in the potential of social networking sites. But they need to understand the demographics of social networking users. Pew Research conducted a survey in late 2012 that addressed these questions.
=+) What do you conclude?Section 14.5
=+e) How many degrees of freedom does it have?f) Find the critical value at a = 0.05.
=+c) What are the expected numbers for each cell if the null hypothesis is true?d) Find the x2 statistic.
=+) What type of test is this?
=+a) What is the null hypothesis?
=+8. A market researcher working for the bank in Exercise 2 wants to know if the distribution of applications by card is the same for the past three mailings. She takes a random sample of 200 from each mailing and counts the number applying for Silver, Gold, and Platinum. The data follow:Type of
=+g) What do you conclude?
=+f) Find the critical value at a = 0.05.
=+e) How many degrees of freedom does it have?
=+c) What are the expected numbers for each cell if the null hypothesis is true?d) Find the x2 statistic.
=+a) What is the null hypothesis?b) What type of test is this?
=+7. An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer.Here are
=+c) What does the answer to part b say about this new group of customers?Exercises M14_SHAR8696_03_SE_C14.indd 495 14/07/14 7:30 AM 496 CHAPTER 14 Inference for Counts: Chi-Square Tests Section 14.4
=+b) Are any of these particularly large? (Compared to what?)
=+a) Compute the standardized residual for each type of card.
=+6. For the data in Exercise 2,
=+c) Why should you have anticipated the answer to part b?
=+b) Are any of these particularly large? (Compared to what?)
=+5. For the data in Exercise 1,a) Compute the standardized residual for each season.
=+e) Using the critical value, what do you conclude about the null hypothesis at a = 0.05?Section 14.3
=+d) Find the a = 0.05 critical value for the x2 distribution with the appropriate number of df.
=+c) What does that say about the null hypothesis?
=+b) Does the statistic you computed in Exercise 2 seem large in comparison to this mean? Explain briefly.
=+4. For the customers in Exercise 2,a) If the customers apply for the three cards according to the historical proportions, about how big, on average, would you expect the x2 statistic to be (what is the mean of the x2 distribution)?
=+e) Using the critical value, what do you conclude about the null hypothesis at a = 0.05?
=+d) Find the a = 0.05 critical value for the x2 distribution with the appropriate number of df.
=+c) What does that say about the null hypothesis?
=+b) Does the statistic you computed in Exercise 1 seem large in comparison to this mean? Explain briefly.
=+ statistic to be (what is the mean of the x2 distribution)?
=+3. For the births in Exercise 1,a) If there is no seasonal effect, about how big, on average, would you expect the x2
=+c) How many degrees of freedom does the x2 statistic have?Section 14.2
=+b) Compute the x2 statistic.
=+a) What is the expected number of customers applying for each type of card in this sample if the historical proportions are still true?
=+2. At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are 60%, 30%, and 10%, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is
=+c) How many degrees of freedom does the x2 statistic have?
=+b) Compute the x2 statistic.
=+a) What is the expected number of births in each season if there is no “seasonal effect” on births?
=+1. If there is no seasonal effect on human births, we would expect equal numbers of children to be born in each season(winter, spring, summer, and fall). A student takes a census of her statistics class and finds that of the 120 students in the class, 25 were born in winter, 35 in spring, 32 in
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+3 Is a student’s social life affected by where the student lives?A campus survey asked a random sample of students whether they lived in a dormitory, in off-campus housing, or at home and whether they had been out on a date 0, 1–2, 3–4, or 5 or more times in the past two weeks.
=+2 Company policy calls for parking spaces to be assigned to everyone at random, but you suspect that may not be so.There are three lots of equal size: lot A, next to the building;lot B, a bit farther away; and lot C on the other side of the highway. You gather data about employees at middle
=+1 A restaurant manager wonders whether customers who dine on Friday nights have the same preferences among the chef’s four special entrées as those who dine on Saturday nights.One weekend he has the wait staff record which entrées were ordered each night. Assuming these customers to be
=+In the call center example (see page 472), examine the residuals to see if any operators stand out as having especially strong or weak performance
=+Is there evidence to suggest that some of the operators are more successful than others?
=+) What other comments could be made about the statistical validity of the test on price comparisons given in the ad?
=+Why do you think WinCo added this statement?
=+) At the bottom of the price list, the following statement appears: “Though this list is not intended to represent a typical weekly grocery order or a random list of grocery items, WinCo continues to be the area’s low price leader.”
=+a) Do the prices listed indicate that, on average, prices at WinCo are lower than prices at Walmart?
=+Dole Fruit Bowl, Mixed Fruit (4 – 4 oz) 1.68 1.98 Progresso Chicken Noodle Soup (19 oz) 1.28 1.38 Precious Mozzarella Ball, Part Skim (16 oz) 3.28 4.23 Mrs. Cubbison Seasoned Croutons (6 oz) 0.88 1.12 Kellogg’s Raisin Bran (20 oz) 1.98 2.50 Campbell’s Soup at Hand, Cream of Tomato(10.75
=+Cube Steak (lb) 3.83 4.11 Beef Top Round London Broil (lb) 3.48 4.12 Pillsbury Devils Food Cake Mix (18.25 oz) 0.88 0.88 Lipton Rice and Sauce Mix (5.6 oz) 0.88 1.06 Sierra Nevada Pale Ale (12 – 12 oz bottles) 12.68 12.84 GM Cheerios Oat Clusters (11.3 oz) 1.98 2.74 Charmin Bathroom Tissue (12
=+products and their price comparison at both WinCo and Walmart are shown in the following table:Item WinCo Price Walmart Price Bananas (lb) 0.42 0.56 Red Onions (lb) 0.58 0.98 Mini Peeled Carrots (1 lb bag) 0.98 1.48 Roma Tomatoes (lb) 0.98 2.67 Deli Tater Wedges (lb) 1.18 1.78
=+84. Grocery prices. WinCo Foods, a large discount grocery retailer in the western United States, promotes itself as the lowest priced grocery retailer. In newspaper ads WinCo Foods published a price comparison for products between WinCo and several competing grocery retailers. One of the
=+b) Was there a statistically significant change in the number of passengers involuntarily denied boarding per 10,000 passengers?
=+a) Are these paired data? Why or why not?
=+like to offend passengers by bumping, so they are constantly trying to improve their systems for predicting how many passengers will show up. Have the rates of “bumping” changed? Here are data on the number of passengers involuntarily denied boarding (“bumping” is not the approved
=+83. Airline “bumping” 2012. Commercial airlines overbook flights, selling more tickets than they have seats, because a sizeable number of reservation holders don’t show up in time for their flights. But sometimes, there are more passengers wishing to board than there are seats. Most
=+) Can we compute the 95% confidence interval for the mean increase in mileage with acetone added? Be sure to check the appropriate assumptions and conditions.
=+) Find a 95% confidence interval for the mean mileage with no additive. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
=+82. Mileage. A recent research states that acetone added to the fuel tank in tiny amounts increases fuel efficiency in cars. Ten randomly selected cars were driven, once without additives and a second time with acetone added. The following miles per gallon were recorded:Car MPG: No additive MPG:
=+b) Find a 95% confidence interval for the mean increase in stopping distance on wet pavement. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
=+a) Find a 95% confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
=+81. Stopping distance. In an experiment on braking performance, a tire manufacturer measured the stopping distance for one of its tire models. On a test track, a car made repeated stops from 60 miles per hour. Twenty tests were run, 10 each on both dry and wet pavement, with results
=+) Explain your findings in a sentence or two in context.
=+b) Find a 95% confidence interval for the mean difference.
=+a) Test the hypothesis that on average, the market value and the sale price of homes from this region are the same.
=+80. Market value. Real estate agents want to set correctly the price of a house that’s about to go on the real estate market. They must choose a price that strikes a balance between one that is so high that the house takes too long to sell and one that’s so low that not enough value will go
=+) These data are actually averages rather than individual times. How might this affect the margins of error in these confidence intervals?
=+b) Estimate the average number of minutes longer a woman must work out at light exertion than at heavy exertion to get the same benefit. Find a 95% confidence interval.
=+a) On average, how many minutes longer than a man must a woman exercise at a light exertion rate in order to burn 200 calories? Find a 95% confidence interval.
=+79. Exercise equipment. A leading manufacturer of exercise equipment wanted to collect data on the effectiveness of their equipment. An August 2001 article in the journal Medicine and Science in Sports and Exercise compared how long it would take men and women to burn 200 calories during light or
=+) Given this information and the results of Exercise 77, what recommendations would you make to the company about the effectiveness of the program?
=+b) Give a 95% confidence interval for the mean change in productivity (as measured by keystrokes per hour).
=+) Is there evidence to suggest that the program increases productivity?
=+78. Employee athletes, part 2. A small company, on hearing about the employee athlete program (see Exercise 77) at the large company down the street, decides to try it as well.To measure the difference in productivity, they measure the average number of keystrokes per hour of 23 employees before
=+c) Give a 95% confidence interval for the mean change in productivity (as measured by keystrokes per hour).
=+) What can you conclude? Explain.
=+a) What are the null and alternative hypotheses?
=+the program increases or decreases productivity. To measure it, they monitor a random sample of 145 employees who word process, measuring their hourly key strokes both before and after the program is instituted. Here are the data:Keystrokes per Hour Before After Difference(After − Before)Mean
=+77. Employee athletes. An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an “employee athlete” program, encouraging every employee to devote 5 minutes an hour to physical activity.The company
=+76. Windy, part 3. Exercises 72 and 74 give summaries and displays for two potential sites for a wind turbine. Test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed.
=+75. Online insurance, part 3. Exercises 71 and 73 give summaries and displays for car insurance premiums quoted by a local agent and an online company. Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company.
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