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mathematics
statistics

Questions and Answers of Statistics

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
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.
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
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
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
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
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
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
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
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.
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
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,
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
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
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
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
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
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%
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
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
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
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-
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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€
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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,
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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 =
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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