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statistics

Introductory Statistics 8th Edition Prem S. Mann - Solutions

Find the following confidence intervals for d, assuming that the populations of paired differences are normally distributed. a. n = 12, = 17.5, sd = 6.3, confidence level = 99% b. n = 27, = 55.9, sd = 14.7, confidence level = 95% c. n = 16, = 29.3, sd = 8.3, confidence level = 90%
Refer to the information given in Exercise 10.3. Test at a 5% significance level if the two population means are different. n1 = 18 1 = 7.82 σ1 = 2.35 n2 = 15 2 = 5.99 σ1 = 3.17
Perform the following tests of hypotheses, assuming that the populations of paired differences are normally distributed. a. H0: µd = 0, H1: µd ≠ 0, n = 9, = 6.7, sd = 2.5, α = .10 b. H0: µd = 0, H1: µd > 0, n = 22, = 14.8, sd = 6.4, α = .05 c. H0: µd = 0, H1: µd < 0, n = 17, = 9.3,
Conduct the following tests of hypotheses, assuming that the populations of paired differences are normally distributed. a. H0: µd = 0, H1: µd ≠ 0, n = 26, = 9.6, sd = 3.9, α = .05 b. H0: µd = 0, H1: µd > 0, n = 15, = 8.8, sd = 4.7, α = .01 c. H0: µd = 0, H1: µd < 0, n = 20, =
A company sent seven of its employees to attend a course in building self-confidence. These employees were evaluated for their self-confidence before and after attending this course. The following table gives the scores (on a scale of 1 to 15, 1 being the lowest and 15 being the highest score) of
Several retired bicycle racers are coaching a large group of young prospects. They randomly select seven of their riders to take part in a test of the effectiveness of a new dietary supplement that is supposed to increase strength and stamina. Each of the seven riders does a time trial on the same
One type of experiment that might be performed by an exercise physiologist is as follows: Each person in a random sample is tested in a weight room to determine the heaviest weight with which he or she can perform an incline press five times with his or her dominant arm (defined as the hand that a
The Bath Heritage Days, which take place in Bath, Maine, have been popular for, among other things, an eating contest. In 2009, the contest switched from blueberry pie to a Whoopie Pie, which consists of two large, chocolate cake-like cookies filled with a large amount of vanilla cream. Suppose the
The manufacturer of a gasoline additive claims that the use of this additive increases gasoline mileage. A random sample of six cars was selected, and these cars were driven for 1 week without the gasoline additive and then for 1 week with the gasoline additive. The following table gives the miles
A factory that emits airborne pollutants is testing two different brands of filters for its smokestacks. The factory has two smokestacks. One brand of filter (Filter I) is placed on one smokestack, and the other brand (Filter II) is placed on the second smokestack. Random samples of air released
What is the shape of the sampling distribution of p̂1 – p̂2 for two large samples? What are the mean and standard deviation of this sampling distribution?
Refer to the information given in Exercise 10.4. Test at a 1% significance level if the two population means are different. n1 = 650 1 = 1.05 σ1 = 5.22 n2 = 675 2 = 1.54 σ1 = 6.80
Construct a 99% confidence interval for p̂1 – p̂2 for the following. n1 = 300, p̂1 = 55, n2 = 200, p̂2 = .62
Construct a 95% confidence interval for p̂1 – p̂2 for the following. n1 = 100, p̂1 = .81, n2 = 150, p̂2 = .77
Refer to the information given in Exercise 10.60. Test at a 1% significance level if the two population proportions are different. n1 = 300, p̂1 = 55, n2 = 200, p̂2 = .62
Refer to the information given in Exercise 10.61. Test at a 5% significance level if p1 p2 is different from zero. n1 = 100, p̂1 = .81, n2 = 150, p̂2 = .77
Refer to the information given in Exercise 10.60. Test at a 1% significance level if p1 is less than p2. n1 = 300, p̂1 = 55, n2 = 200, p̂2 = .62
Refer to the information given in Exercise 10.61. Test at a 2% significance level if p1 is greater than p2. n1 = 100, p̂1 = .81, n2 = 150, p̂2 = .77
A sample of 500 observations taken from the first population gave x1 = 305. Another sample of 600 observations taken from the second population gave x2 = 348. a. Find the point estimate of p1 – p2. b. Make a 97% confidence interval for p1 – p2. c. Show the rejection and non-rejection regions on
A sample of 1000 observations taken from the first population gave x1 = 290. Another sample of 1200 observations taken from the second population gave x2 = 396. a. Find the point estimate of p1 – p2. b. Make a 98% confidence interval for p1 – p2 c. Show the rejection and non-rejection regions
The global recession has led more and more people to move in with relatives, which has resulted in a large number of multigenerational households. An October 2011 Pew Research Center poll showed that 11.5% of people living in multigenerational households were living below the poverty level, and
A November 2011 Gallup poll asked American adults about their views of healthcare and the healthcare system in the United States. Although feelings about the quality of healthcare were positive, the same cannot be said about the quality of the healthcare system. According to this study, 29% of
Refer to the information given in Exercise 10.4. Test at a 5% significance level if µ1 is less than µ2. n1 = 650 1 = 1.05 σ1 = 5.22 n2 = 675 2 = 1.54 σ1 = 6.80
According to Pew Research Center surveys, 79% of U.S. adults were using the Internet in January 2011 and 83% were using it in January 2012 (USA TODAY, January 26, 2012). Suppose that these percentages are based on random samples of 1800 U.S. adults in January 2011 and 1900 in January 2012. a. Let
A state that requires periodic emission tests of cars operates two emission test stations, A and B, in one of its towns. Car owners have complained of lack of uniformity of procedures at the two stations, resulting in different failure rates. A sample of 400 cars at Station A showed that 53 of
The management of a supermarket chain wanted to investigate if the percentages of men and women who prefer to buy national brand products over the store brand products are different. A sample of 600 men shoppers at the company’s supermarkets showed that 246 of them prefer to buy national brand
The lottery commissioner’s office in a state wanted to find if the percentages of men and women who play the lottery often are different. A sample of 500 men taken by the commissioner’s office showed that 160 of them play the lottery often. Another sample of 300 women showed that 66 of them
A mail-order company has two warehouses, one on the West Coast and the second on the East Coast. The company’s policy is to mail all orders placed with it within 72 hours. The company’s quality control department checks quite often whether or not this policy is maintained at the two warehouses.
A company that has many department stores in the southern states wanted to find at two such stores the percentage of sales for which at least one of the items was returned. A sample of 800 sales randomly selected from Store A showed that for 280 of them at least one item was returned. Another
A consulting agency was asked by a large insurance company to investigate if business majors were better salespersons than those with other majors. A sample of 20 salespersons with a business degree showed that they sold an average of 11 insurance policies per week. Another sample of 25
According to an estimate, the average earnings of female workers who are not union members are $909 per week and those of female workers who are union members are $1035 per week. Suppose that these average earnings are calculated based on random samples of 1500 female workers who are not union
An economist was interested in studying the impact of the recession on dining out, including drive thru meals at fast food restaurants. A random sample of forty-eight families of four with discretionary incomes between $300 and $400 per week indicated that they reduced their spending on dining out
According to a report in The New York Times, in the United States, accountants and auditors earn an average of $70,130 a year and loan officers earn $67,960 a year (Jessica Silver Greenberg, The New York Times, April 22, 2012). Suppose that these estimates are based on random samples of 1650
Refer to the information given in Exercise 10.3. Test at a 1% significance level if µ1 is greater than µ2. n1 = 18 1 = 7.82 σ1 = 2.35 n2 = 15 2 = 5.99 σ1 = 3.17
The manager of a factory has devised a detailed plan for evacuating the building as quickly as possible in the event of a fire or other emergency. An industrial psychologist believes that workers actually leave the factory faster at closing time without following any system. The company holds fire
Two local post offices are interested in knowing the average number of Christmas cards that are mailed out from the towns that they serve. A random sample of 80 households from Town A showed that they mailed an average of 28.55 Christmas cards with a standard deviation of 10.30. The corresponding
Refer to Exercise 10.78. Now answer the questions of parts (a) and (b) there without assuming that the standard deviations are the same for the two populations but under the following two situations. a. Using the sample standard deviations given in Exercise 10.78. b. Using sample standard
Repeat Exercise 10.79 assuming that the population standard deviations are not equal for the two groups, but considering the following two situations. a. Using the sample standard deviations given in Exercise 10.79. b. Using a sample standard deviation of $16,700 for accountants and auditors and
Repeat Exercise 10.80 without assuming that the standard deviations for the two populations are the same but considering the following two situations. a. Using the sample standard deviations given in Exercise 10.80. b. Using sample standard deviations of 1.33 and .72 for fire drills and closing
Repeat Exercise 10.81 without assuming that the standard deviations for the two populations are the same but considering the following two situations. a. Using the sample standard deviations given in Exercise 10.81. b. Using sample standard deviations of 6.85 and 11.97 for Town A and Town B,
The owner of a mosquito-infested fishing camp in Alaska wants to test the effectiveness of two rival brands of mosquito repellents, X and Y. During the first month of the season, eight people are chosen at random from those guests who agree to take part in the experiment. For each of these guests,
A random sample of nine students was selected to test for the effectiveness of a special course designed to improve memory. The following table gives the scores in a memory test given to these students before and after this course.a. Construct a 95% confidence interval for the mean d of the
In a random sample of 800 men aged 25 to 35 years, 24% said they live with one or both parents. In another sample of 850 women of the same age group, 18% said that they live with one or both parents. a. Construct a 95% confidence interval for the difference between the proportions of all men and
A November 2011 Pew Research Center poll asked American social media users about their use of social media (such as Facebook, Twitter, MySpace, or LinkedIn). The study is based on a national telephone survey of 2277 adult social media users conducted from April 26 to May 22,
In parts of the eastern United States, whitetail deer are a major nuisance to farmers and homeowners, frequently damaging crops, gardens, and landscaping. A consumer organization arranges a test of two of the leading deer repellents A and B on the market. Fifty-six unfenced gardens in areas having
A May 2011 Harris Interactive poll asked American adult women, “How often do you think women of your age, who have no special risk factors for breast cancer, should have a mammogram to check for breast cancer?” Fifty percent of women age 40 to 49 years and 56% of women age 50 years or older
According to a Randstad Global Work Monitor survey, 52% of men and 43% of women said that working part-time hinders their career opportunities (USA TODAY, October 6, 2011). Suppose that these results are based on random samples of 1350 men and 1480 women. a. Let p1 and p2 be the proportions of all
Manufacturers of two competing automobile models, Gofer and Diplomat, each claim to have the lowest mean fuel consumption. Let µ1 be the mean fuel consumption in miles per gallon (mpg) for the Gofer and µ2 the mean fuel consumption in mpg for the Diplomat. The two manufacturers have agreed to a
Maria and Ellen both specialize in throwing the javelin. Maria throws the javelin a mean distance of 200 feet with a standard deviation of 10 feet, whereas Ellen throws the javelin a mean distance of 210 feet with a standard deviation of 12 feet. Assume that the distances each of these athletes
A new type of sleeping pill is tested against an older, standard pill. Two thousand insomniacs are randomly divided into two equal groups. The first group is given the old pill, and the second group receives the new pill. The time required to fall asleep after the pill is administered is recorded
Gamma Corporation is considering the installation of governors on cars driven by its sales staff. These devices would limit the car speeds to a preset level, which is expected to improve fuel economy. The company is planning to test several cars for fuel consumption without governors for 1 week.
Refer to Exercise 10.95. Suppose Gamma Corporation decides to test governors on seven cars. However, the management is afraid that the speed limit imposed by the governors will reduce the number of contacts the salespersons can make each day. Thus, both the fuel consumption and the number of
Two competing airlines, Alpha and Beta, fly a route between Des Moines, Iowa, and Wichita, Kansas. Each airline claims to have a lower percentage of flights that arrive late. Let p1 be the proportion of Alpha’s flights that arrive late and p2 the proportion of Beta’s flights that arrive
Refer to Exercise 10.56, in which a random sample of six cars was selected to test a gasoline additive. The six cars were driven for 1 week without the gasoline additive and then for 1 week with the additive. The data reproduced here from that exercise show miles per gallon without and with the
Does the use of cellular telephones increase the risk of brain tumors? Suppose that a manufacturer of cell phones hires you to answer this question because of concern about public liability suits. How would you conduct an experiment to address this question? Be specific. Explain how you would
Briefly explain the meaning of independent and dependent samples. Give one example of each of these cases.
A company psychologist wanted to test if company executives have job-related stress scores higher than those of university professors. He took a sample of 40 executives and 50 professors and tested them for job-related stress. The sample of 40 executives gave a mean stress score of 7.6. The sample
A sample of 20 alcoholic fathers showed that they spend an average of 2.3 hours per week playing with their children with a standard deviation of .54 hour. A sample of 25 nonalcoholic fathers gave a mean of 4.6 hours per week with a standard deviation of .8 hour. a. Construct a 95% confidence
Repeat Problem 4 assuming that the times spent per week playing with their children by all alcoholic and all nonalcoholic fathers both are normally distributed with unequal and unknown standard deviations. In Problem 4 A sample of 20 alcoholic fathers showed that they spend an average of 2.3 hours
Lake City has two shops, Zeke€™s and Elmer€™s, that handle the majority of the town€™s auto body repairs. Seven cars that were damaged in collisions were taken to both shops for written estimates of the repair costs. These estimates (in dollars) are shown in the
A sample of 500 male registered voters showed that 57% of them voted in the last presidential election. Another sample of 400 female registered voters showed that 55% of them voted in the same election. a. Construct a 97% confidence interval for the difference between the proportions of all male
Describe the chi-square distribution. What is the parameter (parameters) of such a distribution?
How is the expected frequency of a category calculated for a goodness-of-fit test? What are the degrees of freedom for such a test?
The following table lists the frequency distribution for 60 rolls of a die.Test at a 5% significance level whether the null hypothesis that the given die is fair is true.
In March 2012, the Gallup-Healthways Well-Being Index (www.gallup.com/poll/153251/ No-Major-Change-Americans-Exercise-Habits-2011.aspx) reported on exercise habits of Americans. Specifically, they reported that during 2011, 51.6% of Americans exercised for 30 minutes or more on 3 or more days per
The October 2011 ISACA Shopping on the Job Survey asked employees, €œDuring the holiday season (November and December), how much total time do you think an average employee at your enterprise spends shopping online using a work-supplied computer or smartphone?€ Among those who
A drug company is interested in investigating whether the color of their packaging has any impact on sales. To test this, they used five different colors (blue, green, orange, red, and yellow) for the boxes of an over-the-counter pain reliever, instead of their traditional white box. The following
Over the last 3 years, Art€™s Supermarket has observed the following distribution of modes of payment in the express lines: cash (C) 41%, check (CK) 24%, credit or debit card (D) 26%, and other (N) 9%. In an effort to make express checkout more efficient, Art€™s has just begun
Home Mail Corporation sells products by mail. The company€™s management wants to find out if the number of orders received at the company€™s office on each of the 5 days of the week is the same. The company took a sample of 400 orders received during a 4-week period. The
Of all students enrolled at a large undergraduate university, 19% are seniors, 23% are juniors, 27% are sophomores, and 31% are freshmen. A sample of 200 students taken from this university by the student senate to conduct a survey includes 50 seniors, 46 juniors, 55 sophomores, and 49 freshmen.
Chance Corporation produces beauty products. Two years ago the quality control department at the company conducted a survey of users of one of the company’s products. The survey revealed that 53% of the users said the product was excellent, 31% said it was satisfactory, 7% said it was
Henderson Corporation makes metal sheets, among other products. When the process that is used to make metal sheets works properly, 92% of the metal sheets contain no defects, 5% have one defect each, and 3% have two or more defects each. The quality control inspectors at the company take samples of
Describe in your own words a test of independence and a test of homogeneity. Give one example of each.
Explain how the expected frequencies for cells of a contingency table are calculated in a test of independence or homogeneity. How do you find the degrees of freedom for such tests?
Consider the following contingency table, which is based on a sample survey.a. Write the null and alternative hypotheses for a test of independence for this table. b. Calculate the expected frequencies for all cells, assuming that the null hypothesis is true. c. For Î± = .01, find the
Consider the following contingency table, which records the results obtained for four samples of fixed sizes selected from four populations.a. Write the null and alternative hypotheses for a test of homogeneity for this table. b. Calculate the expected frequencies for all cells assuming that the
During the recent economic recession, many families faced hard times financially. Some studies observed that more people stopped buying name brand products and started buying less expensive store brand products instead. Data produced by a recent sample of 700 adults on whether they usually buy
One hundred auto drivers who were stopped by police for some violations were also checked to see if they were wearing seat belts. The following table records the results of this survey.Test at a 2.5% significance level whether being a man or a woman and wearing or not wearing a seat belt are
Many students graduate from college deeply in debt from student loans, credit card debts, and so on. A sociologist took a random sample of 401 single persons, classified them by gender, and asked, €œWould you consider marrying someone who was $25,000 or more in debt?€ The
During the Bush and Obama administrations, there has been a great deal of discussion about partisanship. Did partisanship have an impact on approval ratings in public polls? The following tables display the approval ratings of both presidents during November of their third year in office
The game show Deal or No Deal involves a series of opportunities for the contestant to either accept an amount of money from the show€™s banker or to decline it and open a specific number of briefcases in the hope of exposing and, thereby eliminating, low amounts of money from the game,
A forestry official is comparing the causes of forest fires in two regions, A and B. The following table shows the causes of fire for 76 randomly selected recent fires in these two regions.Test at a 5% significance level whether causes of fire and regions of fires are related.
National Electronics Company buys parts from two subsidiaries. The quality control department at this company wanted to check if the distribution of good and defective parts is the same for the supplies of parts received from both subsidiaries. The quality control inspector selected a sample of 300
Two drugs were administered to two groups of randomly assigned 60 and 40 patients, respectively, to cure the same disease. The following table gives information about the number of patients who were cured and not cured by each of the two drugs.Test at a 1% significance level whether or not the two
Four hundred people were selected from each of the four geographic regions (Midwest, Northeast, South, West) of the United States, and they were asked which form of camping they prefer. The choices were pop-up camper/trailer, family style (tenting with sanitary facilities), rustic (tenting, no
A December 2011 FOX News poll asked, €œWhich of the following comes closest to your view about what government policy should be toward illegal immigrants currently in the United States?€ The three options were (A) Send all illegal immigrants back to their home country, (B) Have
The following table gives the distributions of grades for three professors for a few randomly selected classes that each of them taught during the last 2 years.Using a 2.5% significance level, test the null hypothesis that the grade distributions are homogeneous for these three professors.
Two random samples, one of 95 blue-collar workers and a second of 50 white-collar workers, were taken from a large company. These workers were asked about their views on a certain company issue. The following table gives the results of the survey.Using a 2.5% significance level, test the null
Determine the value of x2 for 14 degrees of freedom and an area of .10 in the left tail of the chisquare distribution curve.
A sample of certain observations selected from a normally distributed population produced a sample variance of 46. Construct a 95% confidence interval for σ2 for each of the following cases and comment on what happens to the confidence interval of σ2 when the sample size increases. a. n = 12 b. n
A sample of 25 observations selected from a normally distributed population produced a sample variance of 35. Construct a confidence interval for σ2 for each of the following confidence levels and comment on what happens to the confidence interval of σ2 when the confidence level decreases. a. 1
A sample of 22 observations selected from a normally distributed population produced a sample variance of 18. a. Write the null and alternative hypotheses to test whether the population variance is different from 14. b. Using α = .05, find the critical values of x2. Show the rejection and
A sample of 21 observations selected from a normally distributed population produced a sample variance of 1.97. a. Write the null and alternative hypotheses to test whether the population variance is greater than 1.75. b. Using α = .025, find the critical value of x2. Show the rejection and
A sample of 30 observations selected from a normally distributed population produced a sample variance of 5.8. a. Write the null and alternative hypotheses to test whether the population variance is different from 6.0. b. Using α = .05, find the critical value of x2. Show the rejection and
A sample of 18 observations selected from a normally distributed population produced a sample variance of 4.6. a. Write the null and alternative hypotheses to test whether the population variance is different from 2.2. b. Using α = .05, find the critical values of x2. Show the rejection and
Sandpaper is rated by the coarseness of the grit on the paper. Sandpaper that is more coarse will remove material faster. Jobs such as the final sanding of bare wood prior to painting or sanding in between coats of paint require sandpaper that is much finer. A manufacturer of sandpaper rated 220,
The makers of Flippin’ Out Pancake Mix claim that one cup of their mix contains 11 grams of sugar. However, the mix is not uniform, so the amount of sugar varies from cup to cup. One cup of mix was taken from each of 24 randomly selected boxes. The sample variance of the sugar measurements from
An auto manufacturing company wants to estimate the variance of miles per gallon for its auto model AST727. A random sample of 22 cars of this model showed that the variance of miles per gallon for these cars is .62. Assume that the miles per gallon for all such cars are (approximately) normally
The manufacturer of a certain brand of light bulbs claims that the variance of the lives of these bulbs is 4200 square hours. A consumer agency took a random sample of 25 such bulbs and tested them. The variance of the lives of these bulbs was found to be 5200 square hours. Assume that the lives of
Determine the value of x2 for 23 degrees of freedom and an area of .990 in the left tail of the chisquare distribution curve.

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