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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
=+) What does this interval suggest about any gender-based difference in speed?M13_SHAR8696_03_SE_C13.indd 458 14/07/14 7:30 AM Exercises 459
=+c) Find a 95% confidence interval for the difference in the mean number of bread loaves that could be made by men and women.
=+b) Those intervals overlap. What does this suggest about any gender-based difference in speed?
=+a) Find 95% confidence intervals for the average number of bread loaves that males and females can each make.
=+43. Productivity. A bakery hiring people to make bread gives job applicants a test of speed. This test counts how many loaves of bread the applicant can make in a 10-minute period. The table summarizes the data by gender of the job applicant. Assume that all conditions necessary for inference
=+d) Explain why you should not use two separate confidence intervals to decide whether the two leagues differ in average number of runs scored.
=+) With a 95% confidence interval, estimate the mean number of runs scored by National League teams.
=+b) With a 95% confidence interval, estimate the mean number of runs scored by American League teams.
=+a) Create an appropriate display of these data. What do you see?
=+42. Designated hitter 2012. American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in the batting order produces more runs and generates
=+c) Opponents of vitamin supplements continue to insist that it is useless. What type of error do they claim your conclusion makes?
=+b) What is your conclusion about the effectiveness of the supplement?
=+a) What does the P-value mean in this context?
=+41. Supplement test. A pharmaceutical company is producing and marketing a vitamin supplement to help fight infections. In an experiment to test the product, subjects were assigned randomly to take the vitamin supplement or a placebo. The number of days of illness from infections was recorded.
=+grew to hurricane strength changed? Here are those fractions for the same periods as those considered in the previous exercise.1995–2001 2002–2012 0.579, 0.692, 0.429, 0.714, 0.667, 0.571, 0.600 0.333, 0.438, 0.600, 0.556, 0.556, 0.400, 0.500, 0.333, 0.632, 0.333, 0.526a) Write the null and
=+40. Hurricanes 2012. Exercise 39 considered possible changes in the numbers of tropical cyclones that have grown large enough to be officially named. Regardless of the number of storms, has the fraction of named storms that M13_SHAR8696_03_SE_C13.indd 457 14/07/14 7:30 AM 458 CHAPTER 13 Comparing
=+b) Are the conditions for hypothesis testing satisfied?c) If so, test the hypothesis.
=+a) Write the null and alternative hypotheses.
=+. Named tropical cyclones 2012. It has been suggested that global climate change may be affecting the frequency of tropical storms. The data here show the number of tropical cyclones (including hurricanes) assigned official names by the National Hurricane Center. Is there evidence of a
=+Do these results suggest that sales are better after the change in product placement? Test an appropriate hypothesis and state your conclusion. Be sure to check assumptions and conditions.
=+38. Product placement. The owner of a small organic food store was concerned about her sales of a specialty yogurt manufactured in Greece. As a result of increasing fuel costs, she recently had to increase its price. To help boost sales, she decided to place the product on a different shelf(near
=+stem and-leaf display. Do these results suggest that software B is better? Test an appropriate hypothesis and state your conclusion.Software A Software B 12 34 56 78 00 31 30 57 67 25 28 72 522238 43 32 11 33 23 47 66 9987
=+37. Software testing. A professor is about to choose between two statistical software packages for her course. One important criterion in the selection is the ease with which the students learn to use the software. Software A is a menudriven package. Software B is a spreadsheet. The professor
=+c) Is there a significant difference in the mean ages between these two groups? Explain.
=+b) Find the 95% confidence interval for the difference in mean age between the two groups of respondents.
=+and technology give them more control over their lives. A subset of the data from this survey shows the mean ages of two groups of respondents, those who reported that they believed that computers and technology give them “more”control and those that reported “less” control.Group N Mean
=+36. Technology adoption. The Pew Internet & American Life Project (www.pewinternet.org/) conducts surveys to gauge how the Internet and technology impact daily life of individuals, families, and communities. In a recent survey Pew asked respondents if they thought that computers and technology
=+a) Write the null and alternative hypotheses.b) Check the conditions.c) Test the hypothesis and find the P-value.d) Is there a significant difference in 3-year returns between these two kinds of funds?
=+35. Bond funds. Morningstar (www.morningstar.com) selects mutual funds as “Medalist” funds expected to perform well over the long term. You have decided to invest in a bond fund and plan to limit your choice of funds to Morningstar “medalist” funds. But now you must choose
=+d) Is there a significant difference in pH?
=+) Test the hypothesis and find the P-value.
=+b) What conditions would you check?
=+a) Write the null and alternative hypotheses
=+Is there a difference in pH between red and white wines?
=+34. Italian wines. Chemical analyses of 1599 red and 4898 white Italian wines revealed the following summary statistics for pH (a measure of acidity):Type Count Mean St Dev Red 1599 3.311 0.154 White 4898 3.188 0.151
=+d) Is there a significant difference in mean sugar content between these two types of cereals? Explain.
=+. Cereal company. A food company is concerned about recent criticism of the sugar content of their children’s cereals. The data show the sugar content (as a percentage of weight) of several national brands of children’s and adults’cereals.Children’s cereals: 40.3, 55, 45.7, 43.3, 50.3,
=+c) What would you like to see to check the conditions?
=+b) Is there a significant difference in increase in sales between these two groups of stores? Explain.
=+a) Find the 90% confidence interval for the difference in relative increase in sales over this time period.
=+32. Change in sales. Suppose the specialty food chain from Exercise 26 wants to now compare the change in sales across different regions. An examination of the difference in sales over a 37-week period in a recent year for 8 stores in the state of Massachusetts compared to 12 stores in nearby
=+a) Find a 95% confidence interval for the difference in average time for the two routes.b) Which route is better? Explain.
=+31. Airline company. An airline company would like to compare two different routes from Paris to New York. Flights are randomly assigned to two different routes. Thirty flights following Route A report an average of 466 minutes, with a standard deviation of 15 minutes. Thirty flights following
=+30. Lectures. A large university is offering its graduate students a marketing course using two different teaching methods: traditional lecture-based courses and online courses. Students were assigned at random to the two types of courses and then given an exam. The university would like to
=+. CPMP and word problems. The study of the new CPMP mathematics methodology described in Exercise 25 also tested students’ abilities to solve word problems. This table shows how the CPMP and traditional groups performed.What do you conclude? (Assume that the assumptions for inference are
=+28. IT training costs. An accounting firm is trying to decide between IT training conducted in-house and the use of third party consultants. To get some preliminary cost data, each type of training was implemented at two of the firm’s M13_SHAR8696_03_SE_C13.indd 455 14/07/14 7:30 AM 456 CHAPTER
=+c) State a conclusion about the CPMP program.
=+what the P-value means in this context.2-Sample t-Test of m1 - m2 ≠ 0 t-Statistic = -6.451 w/574.8761 df P 6 0.0001
=+b) Here is computer output for this hypothesis test. Explain
=+a) Write an appropriate hypothesis.
=+27. CPMP, again. During the study described in Exercise 25, students in both CPMP and traditional classes took another algebra test that did not allow them to use calculators. The table shows the results. Are the mean scores of the two groups significantly different? Assume that the
=+f) If you computed a 99% confidence interval, would your conclusion in part c change? Explain.
=+e) Would you expect a 99% confidence interval to be wider or narrower? Explain.
=+d) What is the margin of error for this interval?
=+c) Does it appear that one store sells more on average than the other store?
=+) Interpret your interval in context.
=+a) Create a 95% confidence interval for the difference in the mean store weekly sales. (df from technology is 15.31)
=+26. Sales performance. A chain that specializes in healthy and organic food would like to compare the sales performance of two of its primary stores in the state of Massachusetts. These stores are both in urban, residential areas with similar demographics. A comparison of the weekly sales
=+d) Does this result suggest that students who learn mathematics with CPMP will have (statistically) significantly higher mean scores in applied algebra than those in traditional programs? Explain.
=+c) Explain what the calculated interval means in this context.
=+b) If we had created a 98% confidence interval, would the margin of error be larger or smaller?
=+a) What is the margin of error for this confidence interval?
=+25. Learning math. The Core Plus Mathematics Project(CPMP) is an innovative approach to teaching mathematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the performances of CPMP
=+24. Hot dogs and sodium. The Consumer Reports article described in Exercise 23 also listed the sodium content (in mg) for the various hot dogs tested. A test of the null hypothesis that beef hot dogs and meat hot dogs don’t differ in the mean amounts of sodium yields a P-value of 0.110.What
=+23. Hot dogs and calories. Consumers increasingly make food purchases based on nutrition values. Consumer Reports examined the calorie content of two kinds of hot dogs:meat (usually a mixture of pork, turkey, and chicken) and all beef. The researchers purchased samples of several different
=+c) What is the 90% confidence interval for the mean difference?d) What do you conclude at a = 0.05?Chapter Exercises
=+b) How many degrees of freedom does the t-statistic have?
=+a) What is the standard error of the mean difference?
=+machines and tests the combined shut down and restart time of each machine before and after the new operating system has been installed. The mean and standard deviation of the differences (before – after) is 23.5 seconds with a standard deviation of 40 seconds.
=+22. A new operating system is installed in every workstation at a large company. The claim of the operating system manufacturer is that the time to shut down and turn on the machine will be much faster. To test it an employee selects
=+h) What is the P-value associated with this t-statistic.(Assume all conditions for inference are met.)i) At a = 0.01, what is your conclusion?M13_SHAR8696_03_SE_C13.indd 454 14/07/14 7:30 AM Exercises 455
=+g) Is the alternative one- or two-tailed? Comment.
=+) Find the value of the t-statistic.f) How many degrees of freedom does the t statistic have?
=+c) Compute the standard deviation of the difference.d) Compute the standard error of the mean difference.
=+a) Are the data paired? Comment.b) Compute the mean difference.
=+20. A city police department wants to know if the new law enacted to curb traffic violations by its citizens has been effective in decreasing the number of car accidents.They count of the number of accidents a month after the law was passed for each day of the week. Here are the results:Day
=+h) What is the P-value associated with this t-statistic?(Assume that the other assumptions and conditions for inference are met.)i) At a = 0.05, what do you conclude?
=+f) How many degrees of freedom does the t-statistic have?g) Is the alternative one- or two-sided? Explain.
=+) Compute the standard error of the mean difference.e) Find the value of the t-statistic.
=+) Compute the mean difference.c) Compute the standard deviation of the differences.
=+Section 13.7 19. A supermarket chain wants to know if their “buy one, get one free” campaign increases customer traffic enough to justify the cost of the program. For each of 10 stores they select two days at random to run the test. For one of those days (selected by a coin flip), the program
=+c) A manager wants to know if the mean productivity of two workers is the same. For each worker, he randomly selects 30 hours in the past month and compares the number of items produced.
=+b) A real estate agent wants to know how much extra a fireplace adds to the price of a house. She selects 25 city blocks. In each block, she randomly chooses a house with a fireplace and one without and records the assessment value.
=+a) An efficiency expert claims that a new ergonomic desk chair makes typing at a computer terminal easier and faster. To test it, 30 volunteers are selected. Half of the volunteers will use the new chair and half will use their old chairs. Each volunteer types a randomly selected passage for 2
=+18. For each of the following scenarios, say whether the data should be treated as independent or paired samples.Explain briefly. If paired, explain what the pairing involves.
=+c) A manager wants to know if the mean productivity of two workers is the same. For a random selection of 30 hours in the past month, he compares the number of items produced by each worker in that hour.
=+b) A developer wants to know if the houses in two different neighborhoods have the same mean price. She selects 10 houses from each neighborhood at random and tests the null hypothesis that the means are equal.
=+a) An efficiency expert claims that a new ergonomic desk chair makes typing at a computer terminal easier and faster.To test it, 15 volunteers are selected. Using both the new chair and their old chair, each volunteer types a randomly selected passage for 2 minutes and the number of correct words
=+17. For each of the following scenarios, say whether the data should be treated as independent or paired samples.Explain briefly. If paired, explain what the pairing involves.
=+b) Find a 95% confidence interval using the pooled degrees of freedom.M13_SHAR8696_03_SE_C13.indd 453 14/07/14 7:30 AM 454 CHAPTER 13 Comparing Two Meansc) Are your answers different from what you previously found in Exercise 12? Explain briefly why or why not.Section 13.6
=+16. For the data in Exercise 4,a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)
=+c) Are your answers different from what you previously found in Exercise 11? Explain briefly why or why not.
=+b) Find a 95% confidence interval using the pooled degrees of freedom.
=+a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)
=+15. For the data in Exercise 3,
=+c) Are your answers different from what you previously found in Exercise 10? Explain briefly why or why not.
=+b) Find a 95% confidence interval using the pooled degrees of freedom.
=+14. For the data in Exercise 2,a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)
=+c) Are your answers different from what you previously found in Exercise 9? Explain briefly why or why not.
=+b) Find a 95% confidence interval using the pooled degrees of freedom.
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