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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
=+c) Using the information you have, discuss the assumptions and conditions for paired t inference for these data.(Hint: Think hard about the independence assumption in particular.)M13_SHAR8696_03_SE_C13.indd 464 14/07/14 7:30 AM Exercises 465
=+b) Which of the summaries would you use to select between these sites? Why?
=+a) The boxplots show outliers for each site, yet the histogram shows none. Discuss why.
=+74. Windy, part 2. In Exercise 72, we saw summary statistics for wind speeds at two sites near each other, both being considered as locations for an electricity-generating wind turbine. The data, recorded every 6 hours for a year, showed each of the sites had a mean wind speed high enough to
=+c) Using the information you have, discuss the assumptions and conditions for inference with these data.
=+b) The standard deviation of PriceDiff is quite a bit smaller than the standard deviation of prices quoted by either the local or online companies. Discuss why.
=+a) Which of the summaries would help you decide whether the online company offers cheaper insurance? Why?
=+73. Online insurance, part 2. In Exercise 71, we saw summary statistics for 10 drivers’ car insurance premiums quoted by a local agent and an online company. Here are displays for each company’s quotes and for the difference (Local – Online):500 750 1000 1250 Local Online Premium ($)Price
=+Is there a mistake in this output? Why doesn’t the Pythagorean Theorem of Statistics work here? In other words, shouldn’t SD1site2 - site42 = 2SD21site22 + SD21site42?But 213.58622 + 13.42122 = 4.956, not 2.551 as given by the software. Explain why this happened.
=+72. Windy. Alternative sources of energy are of increasing interest throughout the energy industry. Wind energy has great potential. But appropriate sites must be found for the turbines. To select the site for an electricity-generating wind turbine, wind speeds were recorded at several potential
=+At first, the insurance agent wondered whether there was some kind of mistake in this output. He thought the Pythagorean Theorem of Statistics should work for finding the standard deviation of the price differences—in other words, that SD1Local - Online2 = 2SD21Local 2 + SD21Online2.But when
=+His statistical software produced the following summaries(where PriceDiff = Local - Online):Variable Count Mean StdDev Local 10 799.200 229.281 Online 10 753.300 256.267 PriceDiff 10 45.900 175.663 M13_SHAR8696_03_SE_C13.indd 463 14/07/14 7:30 AM 464 CHAPTER 13 Comparing Two Means
=+71. Online insurance. After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving record, etc.)for 10
=+b) Using the test you selected, state your conclusion.
=+a) Which of these tests is appropriate for these data?Explain.
=+70. Cloud seeding. It has long been a dream of farmers to summon rain when it is needed for their crops. Crop losses to drought have significant economic impact. One possibility is cloud seeding in which chemicals are dropped into clouds in an attempt to induce rain. Simpson, Alsen, and Eden
=+e) Use the pooled t-test to test the hypothesis and compare your answer to parts c and d.
=+c) Test the hypothesis and find the P-value.d) What is your conclusion?
=+) Write the null and alternative hypotheses for this test.
=+a) Using the data provided on the CD, check the conditions for this test.
=+69. Designated hitter 2012, part 3. For the same reasons identified in Exercise 42, a friend of yours claims that the average number of home runs hit per game is higher in the American League than in the National League. Using the same 2012 data as in Exercises 42 and 44, you decide to test your
=+e) Use the pooled t-test to test the hypothesis and compare your answer to parts c and d.
=+d) What is your conclusion? Did the sample size make a difference?
=+b) Write the null and alternative hypotheses for this test.c) Test the hypothesis and find the P-value.
=+a) Using the data provided on the CD, check the conditions for this test.
=+68. Real estate, two towns, bigger sample. Residents of one of the towns discussed in Exercise 67 claim that since their town is much smaller, the sample size should be increased. Instead of random sampling 30 homes, you decide to sample 42 homes from the database to test the difference in the
=+c) Test the hypothesis and find the P-value.
=+b) Write the null and alternative hypotheses for this test.
=+67. Real estate, two towns. Residents of neighboring towns in a state in the United States have an ongoing disagreement over who lays claim to the higher average price of a single-family home. Since you live in one of these towns, you decide to obtain a random sample of homes listed for sale
=+d) Find a 95% confidence interval for the mean difference.
=+c) Test the hypothesis and find the P-value if appropriate.
=+b) Write the null and alternative hypotheses for this test.
=+66. Mutual funds returns 2013, part 2. An investor now tells you that if you leave your money in as long as 10 years, you will see an even greater return, so you would like to compare the 5-year and 10-year returns of a random sample of mutual funds to see if your return is expected to be
=+d) Find a 95% confidence interval for the mean difference.
=+b) Write the null and alternative hypotheses for this test.c) Test the hypothesis and find the P-value if appropriate.
=+a) Using the data provided, check the conditions for this test.
=+65. Mutual funds returns 2013. You have heard that if you leave your money in mutual funds for a longer period of time, you will see a greater return. So you would like to compare the 3-year and 5-year returns of a random sample of mutual funds to see if indeed, your return is expected to be
=+b) If you concluded there is a difference, estimate the size of that difference with a 90% confidence interval and explain what your interval means.
=+64. Marketing slogan, part 2. Using the results of the experiment described in Exercise 63, does it matter whether one listens to rap music while studying, or is it better to study without music at all?a) Test an appropriate hypothesis and state your conclusion.
=+b) Create a 90% confidence interval for the mean difference in memory score between students who study to Mozart and those who listen to no music at all. Interpret your interval.
=+a) Does it appear that it is better to study while listening to Mozart than to rap music? Test an appropriate hypothesis and state your conclusion.
=+63. Marketing slogan. A company is considering marketing their classical music as “music to study by.” Is this a valid slogan? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize
=+62. Tee tests, part 2. Given the test results on golf tees described in Exercise 61, is there evidence that balls hit off Stinger tees travel farther? Assume that 6 balls were hit off each tee and that the data are suitable for inference.
=+61. Tee tests. Does it matter what kind of tee a golfer places the ball on? The company that manufactures “Stinger” tees claims that the thinner shaft and smaller head will lessen resistance and drag, reducing spin and allowing the ball to travel farther. Golf Laboratories, Inc. compared the
=+60. Swimming heats 2012. In Exercise 59, we looked at the times in two different heats for the 800-m men’s run from the 2012 Olympics. Unlike track events, swimming heats are not determined at random. Instead, swimmers are seeded so that better swimmers are placed in later heats.Here are the
=+CUB Andy González 106.2 3 GBR Gareth Warburton 107.0 3 HUN Tamás Kazi 107.1 3 GER Sören Ludolph 108.6 3 VAN Arnold Sorina 114.3 3
=+59. Olympic heats 2012. In Olympic running events, preliminary heats are determined by random draw, so we should expect the ability level of runners in the various heats to be about the same, on average. The table gives the times(in seconds) for the 800-m men’s run in the 2012 Olympics in
=+c) Suggest additional factors that may influence pizza sales not accounted for in this exercise.
=+b) Test the null hypotheses and state your conclusion.
=+Do sales appear to be higher during the winter months after omitting those weeks most influenced by football championship games?a) Write the null and alternative hypotheses.
=+58. More pizza sales. Here’s some additional information about the pizza sales data presented in Exercise 57. It is generally thought that sales spike during the weeks leading up to AFC and NFC football championship games, as well as leading up to the Super Bowl at the end of January each year.
=+c) Suggest factors that might have influenced the sales of the frozen pizza during the winter months.
=+b) Construct and interpret a 95% confidence interval for the difference between weekly sales during the winter and summer months.
=+a) How much difference is there between the mean amount of this brand of frozen pizza sold (in pounds) between the two seasons? (Assume that this time frame represents typical sales in the Baltimore area.)
=+57. Pizza sales. A national food product company believes that it sells more frozen pizza during the winter months than during the summer months. Average weekly sales for a sample of stores in the Baltimore area over a three-year period provided the following data for sales volume (in pounds)
=+c) Does this prove that MBA graduates with marketing majors will attract lower starting salaries?
=+b) If this conclusion is incorrect, which type of error was committed?
=+a) Explain what “statistically significant” means in this context.
=+56. MBA salaries. The starting salaries of MBA graduates who majored in finance were compared to the starting salaries of MBA graduates who majored in marketing. It was reported that a significant difference existed between the two majors and that finance majors attract higher salaries than
=+d) What companies might be interested in this information?
=+c) Does this prove that using the Internet at home can improve a student’s performance in science?
=+b) If their conclusion is incorrect, which type of error did the researchers commit?
=+a) Explain what “statistically significant” means in this context.
=+55. The Internet. The National Assessment in Education Program compared science scores for students who had home Internet access with the scores of those who did not, as shown in the graph. They report that the differences are statistically significant.Grade 4 Grade 8 Grade 12 Yes No 100 150 200
=+c) In what way do you think this may have impacted the results?
=+b) Why is this procedure inappropriate? What assumption is violated?
=+a) An analyst for the consumer group computed the twosample t 95% confidence interval for the difference between the two means as 1 -0.71, 4.712. What conclusion would he reach based on this analysis?
=+54. Hybrid SUVs. The Chevy Tahoe Hybrid got a lot of attention when it first appeared. It is a relatively high-priced hybrid SUV that makes use of the latest technologies for fuel efficiency. One of the more popular hybrid SUVs on the market is the modestly priced Ford Escape Hybrid. A consumer
=+d) Suggest a design that could compare immediate brand name recall with recall one day later.M13_SHAR8696_03_SE_C13.indd 460 14/07/14 7:30 AM Exercises 461
=+c) How might the design of this experiment have tainted these results?
=+b) Explain why her procedure was inappropriate. Which of the assumptions for inference was violated?
=+a) Suppose one analyst conducts a two-sample hypothesis test to see if memory of brands advertised during violent TV shows is higher 24 hours later. The P-value is 0.00013.What might she conclude?
=+53. Ad recall. In Exercises 50 and 52, we see the number of advertised brand names people recalled immediately after watching TV shows and 24 hours later. Strangely enough, it appears that they remembered more about the ads the next day. Should we conclude this is true in general about people’s
=+b) Find a 95% confidence interval for the difference in mean number of brand names remembered between the groups watching shows with sexual content and those watching neutral shows. Interpret your interval in this context.
=+a) Is there a significant difference in viewers’ abilities to remember brands advertised in shows with violent vs. neutral content?
=+52. Branding, part 2. In the study described in Exercise 50, the researchers also contacted the subjects again, 24 hours later, and asked them to recall the brands advertised. Results for the number of brands recalled are summarized in the table.Program Type Violent Sexual Neutral No. of
=+b) What advice would you give the company about the upcoming ad campaign?
=+a) At the meeting of the marketing staff, you have to explain what this output means. What will you say?
=+51. Ad campaign. You are a consultant to the marketing department of a business preparing to launch an ad campaign for a new product. The company can afford to run ads during one TV show, and has decided not to sponsor a show with sexual content (see Exercise 50). You create a confidence
=+b) Is there evidence that viewer memory for ads may differ between programs with sexual content and those with neutral content? Test an appropriate hypothesis and state your conclusion.
=+a) Do these results indicate that viewer memory for ads may differ depending on program content? Test the hypothesis that there is no difference in ad memory between programs with sexual content and those with violent content. State your conclusion.
=+50. Branding. The Journal of Applied Psychology reported on a study that examined whether the content of TV shows influenced the ability of viewers to recall brand names of items featured in the commercials. The researchers randomly assigned volunteers to watch one of three programs, each
=+49. Delivery time. A grocery shop offering home delivery is interested in comparing delivery times of their products during two periods of the day: morning and afternoon. They are concerned that car traffic may affect the delivery time. Given the following delivery times (in minutes) of their
=+b) Test an appropriate hypothesis and state your conclusion.
=+a) Identify the procedure you would use to assess the effectiveness of the ERP system and check to see if the conditions allow for the use of that procedure.
=+48. ERP effectiveness. When implementing a packaged Enterprise Resource Planning (ERP) system, many companies report that the module they first install is Financial Accounting. Among the measures used to gauge the effectiveness of their ERP system implementation is acceleration of the
=+b) Test an appropriate hypothesis and state your conclusion.
=+a) Identify the procedure you would use to assess the effectiveness of the birthday gift and check to see if the conditions allow for the use of that procedure.
=+47. Job satisfaction. A company decided to give $100 birthday gifts to its workers to see if this will improve job satisfaction, as measured by a questionnaire that was given to a random sample of workers to assess their satisfaction.Job Satisfaction Index Worker Number Before After 1 25 34 2
=+b) Here are boxplots. What more do they tell you about the distributions? Do you think this changes your conclusions in part a ?Peripherals 21 0–1 Log (price/book)Software
=+a) State and test appropriate hypotheses and state your conclusion. (So you don’t need to compute that strange degrees of freedom formula, the correct df is 36.)
=+46. Technology investment. The Price-to-Book-value ratio is often used by investors to indicate whether a stock’s price is particularly high or low relative to the value of the company. But different market sectors expect different Price/Book values. Here are data on technology companies
=+b) The boxplots of the two distributions show a possible outlier among the data north of Derby. What effect might that have had on your test?2000 1800 1600 1400 1200 Mortality North Derby South
=+a) Test appropriate hypotheses and state your conclusion.
=+. Water hardness. In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in
=+d) Interpret the P-value and state your conclusion. Does the test suggest that the American League scores more runs on average?
=+) Test the hypothesis stated above in part a and find the P-value.
=+44. Designated hitter 2012, part 2. Do the data in Exercise 42 suggest that the American League’s designated hitter rule may lead to more runs per game scored?a) Write the null and alternative hypotheses.b) Find a 95% confidence interval for the difference in mean runs per game, and interpret
=+) Why don’t the results agree?
=+) The two results seem contradictory. Which method is correct: doing two-sample inference, or doing one-sample inference twice?
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