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Business Statistics 3rd Edition Norean Sharpe, Richard Veaux, Paul Velleman - Solutions

Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior citizens. A patient
A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has
Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they will halt the
As in Exercise 33, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards. a) In this context, what is meant by the power of the test the regulators are conducting? b) Will the power be greater if they test 20 or 40 cars? Why?
Consider again the task of the quality control inspectors in Exercise 34. a) In this context, what is meant by the power of the test the inspectors conduct? b) They are currently testing 5 items each hour. Someone has proposed that they test 10 instead. What are the advantages and disadvantages
A company is sued for job discrimination because only 19% of the newly hired candidates were minorities when 27% of all applicants were minorities. Is this strong evidence that the company’s hiring practices are discriminatory? a) Is this a one-tailed or a two- tailed test? Why? b) In this
Highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Volunteers drive through a test course with several of the new-and old-style signs and rate which kind shows up the best. a) Is this a one-tailed or a two-tailed test? Why? b)
A Statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students’ scores. The
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. 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
203 students signed up for the Stats course in Exercise 39. They used the software suggested by the salesman, and scored an average of 108 points on the final with a standard deviation of 8.7 points. a) Should the professor spend the money for this software? Support your recommendation with an
Credit card companies lose money on cardholders who fail to pay their minimum payments. They use a variety of methods to encourage their delinquent cardholders to pay their credit card balances, such as letters, phone calls and eventually the hiring of a collection agency. To justify the cost of
A philanthropic organization sends out “free gifts” to people on their mailing list in the hope that the receiver will respond by sending back a donation. Typical gifts are mailing labels, greeting cards, or post cards. They want to test out a new gift that costs $ 0.50 per item to pro-duce and
The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the company’s safety inspectors have set a standard of ensuring that the stands can support an average of over 500 pounds.
During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient’s leg. It’s important that the company that manufactures the catheter maintain a diameter of 2.00 mm. (The standard deviation is quite small.) Each day, quality
The manufacturer of the metal TV stands in Exercise is thinking of revising its safety test. a) If the company’s lawyers are worried about being sued for selling an unsafe product, should they increase or decrease the value of a? Explain. b) In this context, what is meant by the power of the
The catheter company in Exercise 44 is reviewing its testing procedure. a) Suppose the significance level is changed to α = 0.01. Will the probability of a Type II error increase, decrease, or remain the same? b) What is meant by the power of the test the company conducts? c) Suppose the
In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%- or the 30%-head coin. Your
You are in charge of shipping computers to customers. You learn that a faulty RAM chip was put into some of the machines. There’s a simple test you can perform, but it’s not perfect. All but 4% of the time, a good chip passes the test, but unfortunately, 35% of the bad chips pass the test, too.
For each of the following situations, find the critical value(s) for z or t. a) H0: p = 0.5 vs. HA: p ≠ 0.5 at α = 0.05. b) H0: p = 0.4 vs. HA: p > 0.4 at α = 0.05. c) H0: μ = 10 vs. HA: μ ≠ 10 at α = 0.05; n = 36. d) H0: p = 0.5 vs. HA: p > 0.5 at α = 0.01; n = 345. e) H0: μ = 20
The philanthropic organization of Exercise 42 decided to go ahead with the new gift. In mailings to 98,000 prospects, the new mailing yielded an average of $ 0.78. If they had decided based on their initial trial not to use this gift, what kind of error would they have made? What aspects of their
SLIX wax is developing a new high performance fluorocarbon wax for cross country ski racing designed to be used under a wide variety of conditions. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time to finish their standard test course should
Pop’s Popcorn, Inc. needs to determine the optimum power and time settings for their new licorice-flavored 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 that their
For each of the following situations, find the critical value for z or t. a) H0: μ = 105 vs. HA: μ ≠ 105 at α = 0.05; n = 61. b) H0: p = 0.05 vs. HA: p > 0.05 at α = 0.05. c) H0: p = 0.6 vs. HA: p ≠ 0.6 at α = 0.01. d) H0: p = 0.5 vs. HA: p < 0.5 at α = 0.01; n = 500. e) H0: p = 0.2
Suppose that you are testing the hypotheses H0: p = 0.20 vs. HA: p ≠ 0.20. A sample of size 250 results in a sample proportion of 0.25.a) Construct a 95% confidence interval for p.b) Based on the confidence interval, at α = .05 can you reject H0? Explain.c) What is the difference between the
Suppose that you are testing the hypotheses H0: p = 0.40 vs. HA: p > 0.40. A sample of size 200 results in a sample proportion of 0.55.a) Construct a 90% confidence interval for p.b) Based on the confidence interval, at α = .05 can you reject H0? Explain.c) What is the difference between the
Suppose that you are testing the hypotheses H0: μ = 16 vs. HA: μ < 16. A sample of size 25 results in a sample mean of 16.5 and a standard deviation of 2.0. a) What is the standard error of the mean? b) What is the critical value of t* for a 90% confidence interval? c) Construct a 90%
Does it matter what kind of tee a golfer places the ball on? The company that manufactures €œStinger€ 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
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.
A company is considering marketing their classical music as €œmusic 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 objects
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) If you concluded there is a difference, estimate the size of
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 greater if you leave your money in
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 greater if you leave your money in the funds
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 with a major local realtor to
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 mean price of single-family homes in these two
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 friend’s theory.a) Using the data
Using the data in Exercise 3, test the hypothesis that the mean age of houses in the two neighborhoods is the same. You may assume that the ages of houses in each neighborhood follow a Normal distribution. a) Calculate the P-value of the statistic knowing that the approximation formula gives 62.2
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 (Techno metrics, 1975)
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 of his clients and
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):a) Which of the summaries would help you decide
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 qualify, but how can we
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.In exercise 73In exercise 73
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.In exercise 72In exercise 74
An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an €œemployee athlete€ program, encouraging every employee to devote 5 minutes an hour to physical activity. The company worries
A small company, on hearing about the employee athlete program (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 and after the program is instituted.
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 heavy workouts on various
Using the data in Exercise 4, test the hypothesis that the mean number of page views from the two websites is the same. You may assume that the number of page views from each website follow a Normal distribution. a) Calculate the P-value of the statistic knowing that the approximation formula gives
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 to the homeowner. One
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 shown in the table. (Note that actual
For another test of the tires in Exercise 81, the company tried them on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the following table.a) Find a 95% confidence interval for the mean dry pavement stopping distance. Be sure to
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 airlines try to entice travelers
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 retailers compared against
Using the data in Exercise 1, and assuming that the data come from a distribution that is normally distributed, a) Find a 95% confidence interval for the mean difference in ages of houses in the two neighborhoods. b) Is 0 within the confidence interval? c) What does it say about the null hypothesis
A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The table shows the data for each sample (in years). Neighborhood 1
Using the data in Exercise 2, and assuming that the data come from a distribution that is normally distributed, a) Find a 95% confidence interval for the mean difference in page views from the two websites. b) Is 0 within the confidence interval? c) What does it say about the null hypothesis that
Using the summary statistics in Exercise 3, and assuming that the data come from a distribution that is normally distributed, a) Find a 95% confidence interval for the mean difference in ages of houses in the two neighborhoods using the df given in Exercise 7. b) Why is the confidence interval
Using the summary statistics in Exercise 4, and assuming that the data come from a distribution that is normally distributed, a) Find a 95% confidence interval for the mean difference in page views from the two websites. b) Why is the confidence interval narrower than the one you found in Exercise
For the data in Exercise 1,a) Test the null hypothesis at α = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)b) Find a 95% confidence interval using the pooled degrees of freedom.c) Are your answers different from what you previously found in Exercise 9? Explain
For the data in Exercise 2,a) Test the null hypothesis at α = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)b) Find a 95% confidence interval using the pooled degrees of freedom.c) Are your answers different from what you previously found in Exercise 10? Explain
For the data in Exercise 3,a) Test the null hypothesis at α = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)b) Find a 95% confidence interval using the pooled degrees of freedom.c) Are your answers different from what you previously found in Exercise 11? Explain
For the data in Exercise 4,a) Test the null hypothesis at α = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)b) Find a 95% confidence interval using the pooled degrees of freedom.c) Are your answers different from what you previously found in Exercise 12? Explain
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. a) An efficiency expert claims that a new ergonomic desk chair makes typing at a computer terminal easier and faster. To test
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. a) An efficiency expert claims that a new ergonomic desk chair makes typing at a computer terminal easier and faster. To test
A supermarket chain wants to know if their €œbuy 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 will be in
A market analyst wants to know if the new website he designed is showing increased page views per visit. A customer is randomly sent to one of two different websites, offering the same products, but with different designs. Here are the page views from five randomly chosen customers from each
A city wants to know if a new advertising campaign to make citizens aware of the dangers of driving after drinking has been effective. They count the number of drivers who have been stopped with more alcohol in their systems than the law allows for each day of the week in the week before and the
In order to judge whether the program is successful, the manager of the supermarket chain in Exercise 21 wants to know the plausible range of values for the mean increase in customers using the program. Construct a 90% confidence interval.
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 36 machines and tests the combined shut down and restart time of each
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 brands. The meat hot dogs averaged
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 would you conclude?
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 students with those taught
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 randomly sampled over a period
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 assumptions for inference are
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 offices located in different cities. The table below shows the average
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 met.)
The developer in Exercise 1 hires an assistant to collect a random sample of houses from each neighborhood and finds that the summary statistics for the two neighborhoods look as follows:Neighborhood 1Neighborhood 2n1 = 30 ........ n2 = 35y1 = 57.2 yrs ....... y2 = 47.6 yrss1 = 7.51 yrs ....... s2
The accounting firm described in Exercise 28 is interested in providing opportunities for its auditors to gain more expertise in statistical sampling methods. They wish to compare traditional classroom instruction with online self-paced tutorials. Auditors were assigned at random to one type of
A trucking company would like to compare two different routes for efficiency. Truckers are randomly assigned to two different routes. Twenty truckers following Route A report an average of 40 minutes, with a standard deviation of 3 minutes. Twenty truckers following Route B report an average of 43
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 states reveals the
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, 45.9, 53.5, 43, 44.2,
Chemical analyses of 1599 red and 4898 white Italian wines revealed the following summary statistics for pH (a measure of acidity):Is there a difference in pH between red and white wines?a) Write the null and alternative hypothesesb) What conditions would you check?c) Test the hypothesis and find
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 between a taxable fund and a
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 give people more or less
A company is producing and marketing new reading activities for elementary school children that it believes will improve reading comprehension scores. A researcher randomly assigns third graders to an eight-week program in which some will use these activities and others will experience traditional
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 eye level for most
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 change?a) Write the null and alternative
Not happy with the previous results, the analyst in Exercise 2 takes a much larger random sample of customers from each website and records their page views. Here are the data:Website AWebsite Bn1 = 80 ..........n2 = 95y1 = 7.7 pages.....y2 = 7.3 pagess1 = 4.6 pages .....s2 = 4.3 pagesa) Find the
Exercise 39 considered possible changes in the numbers of tropical cyclones that have grown large enough to be officially named.In exercise 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
A pharmaceutical company is producing and marketing a ginkgo biloba supplement to enhance memory. In an experiment to test the product, subjects were assigned randomly to take ginkgo biloba supplements or a placebo. Their memory was tested to see whether it improved. Here are boxplots comparing the
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 more interest among fans. The
A factory hiring people to work on an assembly line gives job applicants a test of manual agility. This test counts how many strangely shaped pegs the applicant can fit into matching holes in a one-minute period. The table summarizes the data by gender of the job applicant. Assume that all
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 your interval.c) Test the hypothesis
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 the drinking water.
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 (biz.yahoo.com/p/8conameu.html
A company institutes an exercise break for 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.a) Identify the procedure you would use to assess the effectiveness of the exercise program
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 financial close process. Below is a
A small appliance company is interested in comparing delivery times of their product during two months. They are concerned that the summer slow-downs in August cause delivery times to lag during this month.Given the following delivery times (in days) of their appliances to the customer for a random
For the data in Exercise 1, we want to test the null hypothesis that the mean age of houses in the two neighborhoods is the same. Assume that the data come from a population that is Normally distributed.a) Using the values you found in Exercise 1, find the value of the t-statistic for the
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 containing the same
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 interval for the difference
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.a) Is there a significant difference in viewers€™ abilities to

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