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Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions
Using the sample results in Exercise 10.76, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized proportion (0.41) within the interval? Given the presence or absence of the 0.41 value within the interval, is this consistent with the findings of the
Website administrators sometimes use analysis tools or service providers to “track” the movements of visitors to the various portions of their site. Overall, the administrator of a political action website has found that 35% of the visitors who visit the “Environmental Issues” page go on to
What is a power curve and how is it applicable to hypothesis testing?
A state representative is reported as saying that about 10% of reported auto thefts involve owners whose cars have not really been stolen, but who are trying to defraud their insurance company. What null and alternative hypotheses would be appropriate in evaluating the statement made by this
What is an operating characteristic curve and how is it related to the power curve for a test?
For the test described in Exercise 10.31, if the true population mean is really 2.520 inches, what is the probability that the inspector will correctly reject the false null hypothesis that μ = 2.500 inches? In exercise Following maintenance and calibration, an extrusion machine produces aluminum
For the test described in Exercise 10.32, assume that the true population mean for the new booklet is μ = 2.80 hours. Under this assumption, what is the probability that the false null hypothesis, H0: μ ≥ 3.00 hours, will be rejected? In exercise A manufacturer of electronic kits has found that
Using assumed true population means of 2.485, 2.490, 2.495, 2.500, 2.505, 2.510, and 2.515 inches, plot the power curve for the test in Exercise 10.31. In exercise Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with
Using assumed true population means of 2.80, 2.85, 2.90, 2.95, and 3.00 hours, plot the power curve for the test in Exercise 10.32. In exercise A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3 hours, with a standard
Using assumed true population percentages of 2%, 3%, 4%, 5%, 6%, and 7%, plot the power curve for the test in Exercise 10.63. In exercise A simple random sample of 300 items is selected from a large shipment, and testing reveals that 4% of the sampled items are defective. The supplier claims that
When a thread-cutting machine is operating properly, only 2% of the units produced are defective. Since the machine was bumped by a forklift truck, however, the quality-control manager is concerned that it may require expensive downtime and a readjustment. The manager would like to set up a
Plot the operating characteristic curve that corresponds to the power curve constructed for Exercise 10.84. In exercise 10.84 Using assumed true population means of 2.485, 2.490, 2.495, 2.500, 2.505, 2.510, and 2.515 inches, plot the power curve for the test in Exercise 10.31. In exercise
Plot the operating characteristic curve that corresponds to the power curve constructed for Exercise 10.86. In exercise 10.86 Using assumed true population percentages of 2%, 3%, 4%, 5%, 6%, and 7%, plot the power curve for the test in Exercise 10.63. In exercise 10.63 A simple random sample of 300
For each of the following situations, determine whether a one-tail test or a two-tail test would be appropriate. Describe the test, including the null and alternative hypotheses, then explain your reasoning in selecting it. a. A machine that has not been serviced for several months is producing
Strands of human hair absorb elements from the bloodstream and provide a historical record of both health and the use or nonuse of chemical substances. Hair grows at the rate of about one-half inch per month, and a person with long hair might be accused or absolved on the basis of a segment of hair
Before accepting a large shipment of bolts, the director of an elevator construction project checks the tensile strength of a simple random sample consisting of 20 bolts. She is concerned that the bolts may be counterfeits, which bear the proper markings for this grade of bolt, but are made from
Before the hiring of an efficiency expert, the mean productivity of a firm’s employees was 45.4 units per hour, with a standard deviation of 4.5 units per hour. After incorporating the changes recommended by the expert, it was found that a sample of 30 workers produced a mean of 47.5 units per
The average U.S. family includes 3.13 persons. To determine whether families in her city tend to be representative in size compared to those across the United States, a city council member selects a simple random sample of 40 families. She finds the average number of persons in a family to be 3.40,
The average U.S. household has $235,600 in life insurance. A local insurance agent would like to see how households in his city compare to the national average, and selects a simple random sample of 30 households from the city. For households in the sample, the average amount of life insurance is
Technical data provided with a room dehumidifier explain that units tested from the production line consume a mean of 800 watts of power, with a standard deviation of 12 watts. The superintendent of a large office complex, upon evaluating 30 of the units recently purchased and finding their mean
A regional office of the Internal Revenue Service randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Jeffrey Jones, is suspected of being
A state transportation official claims that the mean waiting time at exit booths from a toll road near the capitol is no more than 0.40 minutes. For a sample of 35 motorists exiting the toll road, it was found that the mean waiting time was 0.46 minutes, with a standard deviation of 0.16 minutes.
During 2006, 3.0% of all U.S. households were burglary victims. For a simple random sample of 300 households from a certain region, suppose that 18 households were victimized by burglary during that year. Apply an appropriate hypothesis test and the 0.05 level of significance in determining whether
The first item on Ted Thorndikes agenda for today is a meeting with Martha Scott, a technical sales representative with Cromwell Industries. Cromwell produces a racquet-stringing machine that is promoted as being the fastest in the industry. In their recent telephone conversation,
The Springdale computer database exercise of Chapter 2 listed 30 shopping-related questions asked of 150 respondents in the community of Springdale. The data are in file SHOPPING. The coding key for these responses was also provided in the Chapter 2 exercise. In this section, hypothesis testing
Pronto Pizza is a family-owned pizza restaurant in Vinemont, a small town of 20,000 people in upstate New York. Antonio Scapelli started the business 30 years ago as Antonio’s Restaurant with just a few thousand dollars. Antonio, his wife, and their children, most of whom are now grown, operate
In a test of the effectiveness of a new battery design, 16 battery-powered music boxes are randomly provided with either the old design or the new version. Hours of playing time before battery failure were as follows:Assuming normal populations with equal standard deviations, use the 0.05 level to
The data in file XR11100 are the weights (in grams) for random samples of grain packages filled by two different filling machines. The machines have a fine adjustment for the mean amount of fill, but the standard deviations are inherent in the design of the grain delivery mechanism. Based on these
An anthropologist studying personal advertisements in a Utica, New York, newspaper has observed whether the advertiser included a mention of an interest in the outdoors in his or her ads. According to the anthropologist, citing the outdoors “may be taken to imply not only good life habits, but
A nutritionist has noticed a FoodFarm ad stating the company’s peanut butter contains less fat than that produced by a major competitor. She purchases 11 8-ounce jars of each brand and measures the fat content of each. The 11 FoodFarm jars had an average of 31.3 grams of fat, with a standard
A study published in the Archives of Internal Medicine examined the prevalence of so-called “difficult” patients who ask for unneeded prescriptions, unnecessarily complain, or otherwise cause extraordinary frustrations for their medical provider. Researchers found the mean age of doctors having
It has been claimed that flattening (“rolling”) the barrel of a graphite baseball bat can stretch the fibers and result in a pitched baseball being returned faster than with a regulation bat. This was a controversial topic during the 2009 baseball College World Series. Assume that data file
Comparing the number of Facebook “friends” for men and women, observers have speculated about whether the mean number of friends could be the same for each group. Assume that data file XR11014 lists the number of Facebook friends for independent samples of male and female Facebook users. Based
Using the sample results in Exercise 11.14, construct and interpret the 95% confidence interval for the difference between the population means. Is the hypothesized difference (0.00) within the interval? Given the presence or absence of the 0.00 value within the interval, is this consistent with
An engineer has measured the hardness scores for a sample of conveyor-belt support bearings that have been hardened by two different methods. The first method is used by her company, and the second method is known to be used by a number of other companies in the industry. With the resulting data in
Using the sample results in Exercise 11.16, construct and interpret the 95% confidence interval for the difference between the population means. Is the hypothesized difference (0.00) within the interval? Given the presence or absence of the 0.00 value within the interval, is this consistent with
In two independent samples from populations that are normally distributed, x-bar1 = 35.0, s1 = 5.8, n1 = 12 and x-bar2 = 42.5, s2 = 9.3, n2 = 14. Using the 0.05 level of significance, test H0: μ1 = μ2 versus H1: μ1 ≠ μ2.
In two independent samples, x-bar1 = 165.0, s1 = 21.5, n1 = 40 and x-bar2 = 172.9, s2 = 31.3, n2 = 32. Using the 0.10 level of significance, test H0: μ1 ≥ μ2 versus H1: μ1 < μ2.
An educator is considering two different videotapes for use in a half-day session designed to introduce students to the basics of economics. Students have been randomly assigned to two groups, and they all take the same written examination after viewing the videotape. The scores are summarized
In two independent samples, x-bar1 = 125.0, s1 = 21.5, n1 = 40, and x-bar2 = 116.4, s2 = 10.8, n2 = 35. Using the 0.025 level of significance, test H0: μ1 ≤ μ2 versus H1: μ1 > μ2.
Fred and Martina, senior agents at an airline security checkpoint, carry out advanced screening procedures for hundreds of randomly selected passengers per day. For a random sample of 30 passengers recently processed by Fred, the mean processing time was 124.5 seconds, with a standard deviation of
A tire company is considering switching to a new type of adhesive designed to improve tire reliability in high-temperature and overload conditions. In laboratory “torture” tests with temperatures and loads 90% higher than the maximum normally encountered in the field, 15 tires constructed with
The credit manager for Braxton’s Department Store, in examining the accounts for various types of customers served by the establishment, has noticed that the mean outstanding balance for a sample of 20 customers from the local ZIP code is $375, with a standard deviation of $75. For a sample of 25
Safety engineers at a manufacturing plant are evaluating two brands of 50-ampere electrical fuses for possible purchase and use in the plant. One of the performance characteristics they are considering is how long the fuse will carry 50 amperes before it blows. In a sample of 35 fuses from the
According to a national Gallup poll, men visit the doctor’s office an average of 3.8 times per year, while women visit an average of 5.8 times per year. In a similar poll conducted in a Midwest county, a sample of 50 men visited the doctor an average of 2.2 times in the past year, with a standard
One of the measures of the effectiveness of a stimulus is how much the viewer’s pulse rate increases on exposure to it. In testing a lively new music theme for its television commercials, an advertising agency shows ads with the new music to a sample of 25 viewers. Their mean pulse rate increase
According to a Yankelovich poll, women spend an average of 19.1 hours shopping during the month of December, compared to 12.7 hours for men. Assuming that file XR11027 contains the survey data underlying these results, use the 0.01 level in examining whether the sample mean for women is
When companies are designing a new product, one of the steps typically taken is to see how potential buyers react to a picture or prototype of the proposed product. The product-development team for a notebook computer company has shown picture A to a large sample of potential buyers and picture B
It has been reported that the average visitor from Japan spent $3120 during a trip to the United States, while the average for a visitor from the United Kingdom was $2654. Assuming that file XR11029 contains the survey data underlying these results, use the 0.05 level in examining whether the
Using independent random samples, a researcher is comparing the number of hours of television viewed last week for high school seniors versus sophomores. The results are shown here. Assuming normal populations with equal standard deviations, does it appear that the average number of television
During May 2009, visitors to usatoday.com spent an average of 12.2 minutes per visit, compared to 11.0 minutes for visitors to washingtonpost.com. Assuming that file XR11030 contains the sample data underlying these results, use the 0.01 level of significance in examining whether the population
For the following independent random samples, use the z-test and the 0.01 level of significance in testing H0: μ1 = μ2 versus H1: μ1 μ2.
For the following independent random samples, use the z-test and the 0.05 level of significance in testing H0: μ1 ¤ μ2 versus H1: μ1 > μ2.
Repeat Exercise 11.20 using the z-test approximation to the unequal-variances t-test. Repeat Exercise 11.20 In two independent samples, x-bar1 = 125.0, s1 = 21.5, n1 = 40, and x-bar2 = 116.4, s2 = 10.8, n2 = 35. Using the 0.025 level of significance, test H0: μ1 ≤ μ2 versus H1: μ1 > μ2.
Repeat Exercise 11.21 using the z-test approximation to the unequal-variances t-test. Repeat exercise 11.21 Fred and Martina, senior agents at an airline security checkpoint, carry out advanced screening procedures for hundreds of randomly selected passengers per day. For a random sample of 30
According to the U.S. Bureau of Labor Statistics, personal expenditures for entertainment fees and admissions averaged $349 per person in the Northeast and $420 in the West. Assuming that these data involved (1) sample sizes of 800 and 600 and (2) standard deviations of $215 and $325, respectively,
Surveys of dog owners in two adjacent towns found the average veterinary-related expense total for dog owners in town A during the preceding year was $240, with a standard deviation of $55, while the comparable results in nearby town B were $225 and $32, respectively. Assuming a sample size of 30
A study of 102 patients who had digestive-tract surgery found that those who chewed a stick of gum for 15 minutes at mealtimes ended up being discharged after an average of 4.4 days in the hospital, compared to an average of 5.2 days for their counterparts who were not provided with gum. Assuming
A study found that women of normal weight missed an average of 3.4 days of work due to illness during the preceding year, compared to an average of 5.2 days for women who were considered overweight. Assuming (1) a sample size of 30 for each group and (2) sample standard deviations of 2.5 and 3.6
An ambulance service located at the edge of town is responsible for serving a large office building in the downtown area. Testing different routes for getting from the ambulance station to the office building, a driver finds that five trips using route A take an average of 5.9 minutes, with a
According to a psychologist at the Medical College of Virginia, soccer players who “head” the ball 10 or more times a game are at risk for brain damage that could lower their intellectual abilities. In tests involving young male soccer players, those who typically headed the ball 10 or more
In their 2003 and 2008 studies on how long wireless customers have to spend on hold before speaking with a customer service representative, J.D. Power and Associates found the mean times to be 3.3 minutes and 4.4 minutes, respectively. Assume that data file XR11041 contains the data, in minutes,
In planning the processes to be incorporated into a new manufacturing facility, engineers have proposed two possible assembly procedures for one of the phases in the production sequence. Sixty of the eventual production line workers have taken part in preliminary tests, with data representing
A study has been conducted to examine the effectiveness of a new experimental program for preparing high school students for the Scholastic Aptitude Test. Eighty students have been randomly divided into two groups of 40. The eventual SAT scores for those exposed to the new program and the
A trucking firm is considering the installation of a new, low-restriction engine air filter for its long-haul trucks, but doesnt want to make the switch unless the new filter can be shown to improve the fuel economy of these vehicles. A test is set up in which each of 10 trucks makes
In an attempt to measure the emotional effect of a proposed billboard ad, an advertising agency checks the pulse rate of 10 persons before and after they are shown a photograph of the billboard. The agency believes that an effective billboard will increase the pulse rate of those who view it. In
The students in an aerobics class have been weighed both before and after the 5-week class, with the following results:Using the 0.05 level of significance, evaluate the effectiveness of the program. Using the appropriate statistical table, what is the most accurate statement we can make about the
A maintenance supervisor is comparing the standard version of an instructional booklet with one that has been claimed to be superior. An experiment is conducted in which 26 technicians are divided into two groups, provided with one of the booklets, then given a test a week later. For the 13 using
For a special pre–New Year’s Eve show, a radio station personality has invited a small panel of prominent local citizens to help demonstrate to listeners the adverse effect of alcohol on reaction time. The reaction times (in seconds) before and after consuming four drinks are in data file
A plant manager has collected productivity data for a sample of workers, intending to see whether there is a difference in the number of units they produce on Monday versus Thursday. The results (units produced) are in data file XR11051. Using the 0.01 level of significance, evaluate the null
Summary data for two independent samples are p1 = 0.36, n1 = 150, and p2 = 0.29, n2 = 100. Use the 0.025 level of significance in testing H0: π1 ≤ π2 versus H1: π1 > π2.
Summary data for two independent samples are p1 = 0.31, n1 = 400, and p2 = 0.38, n2 = 500. Use the 0.05 level of significance in testing H0: π1 = π2 versus H1: π1 ≠ ≠2.
A bank manager has been presented with a new brochure that was designed to be more effective in attracting current customers to a personal financial counseling session that would include an analysis of additional banking services that could be advantageous to both the bank and the customer. The
In examining the ability of users to complete a variety of information-seeking tasks on their mobile devices, Nielsen Norman Group assigned sample members to get the answers to a variety of questions like, “How many calories are there typically in a slice of thincrust pizza?” The success rate
In a study by the United Dairy Industry Association, 42% of 655 persons age 35–44 said they seldom or never ate cottage cheese. For 455 individuals age 45–54, the corresponding percentage was 34%. At the 0.01 level, can we reject the possibility that the population percentages could be equal
During the course of a year, 38.0% of the 213 merchant ships lost were general cargo carriers, while 43.8% of the 219 ships lost during the following year were in this category. Using a two-tail test at the 0.05 level, examine whether this difference could have been the result of chance variation
Of 200 subjects approached by interviewer A, 45 refused to be interviewed. Of 120 approached by interviewer B, 42 refused an interview. At the 0.05 level of significance, can we reject the possibility that the interviewers are equally capable of obtaining interviews?
Community National Bank is using an observational study to examine the utilization of its new 24-hour banking machine. Of 300 males who used the machine last week, 42% made two or more transactions before leaving. Of 250 female users during the same period, 50% made at least two transactions while
A sample of 40 investment customers serviced by an account manager are found to have had an average of $23,000 in transactions during the past year, with a standard deviation of $8500. A sample of 30 customers serviced by another account manager averaged $28,000 in transactions, with a standard
A telephone sales solicitor, trying to decide between two alternative sales pitches, randomly alternated between them during a day of calls. Using approach A, 20% of 100 calls led to requests for the mailing of additional product information. For approach B in another 100 calls, only 14% led to
In a preliminary study, the U.S. Veterans Affairs Department found that 30.9% of the 81 soldiers who were near an accidental nerve gas release just after the 1991 Persian Gulf War had muscle and bone ailments, compared to a rate of 23.5% for the 52,000 Gulf veterans who were not near that area. Use
According to the ICR Research Group, 63% of Americans in the 18–34 age group say they are comfortable filing income tax returns electronically, compared to just 49% of those who are 55–64. Using the 0.025 level of significance, and assuming there were 200 persons surveyed from each age group,
An American Express survey of small-business owners found that 71% of female owners feel stressed by their work/life balance, compared to 62% of their male counterparts. Assume that file XR11063 contains the underlying sample data for female and male smallbusiness owners, respectively, with the
Attempting to improve the quality of services provided to customers, the owner of a chain of high-fashion department stores randomly selected a number of clerks for special training in customer relations. Of this group, only 10% were the subject of complaints to the store manager during the 3
A study by the National Marine Manufacturers Association found that 12.2% of those who participated in sailing were females age 25–34. Of those who participated in horseback riding during the same period, 14.7% were females in this age group. Assume that file XR11065 contains the underlying data
For two samples from what are assumed to be normally distributed populations, the sample sizes and standard deviations are n1 = 10, s1 = 23.5, n2 = 9, and s2 = 10.4. At the 0.10 level of significance, test the null hypothesis that the population variances are equal. Would your conclusion be
For two samples from what are assumed to be normally distributed populations, the sample sizes and standard deviations are n1 = 28, s1 = 103.1, n2 = 41, and s2 = 133.5. At the 0.10 level of significance, test the null hypothesis that the population variances are equal. Would your conclusion be
Given the information in Exercise 11.10, and using the 0.02 level of significance in comparing the sample standard deviations, were we justified in assuming that the population standard deviations are equal? Would your conclusion change if the standard deviation of playing times for music boxes
Given the information in Exercise 11.11, and using the 0.05 level of significance in comparing the sample standard deviations, were we justified in assuming that the population standard deviations were equal? Would your conclusion change if the standard deviation for the FoodFarm jars had been 3.0
Comparing dexterity-test scores of workers on the day shift versus those on the night shift, the production manager of a large electronics plant finds that a sample of 37 workers from the day shift have an average score of 73.1, with a standard deviation of 12.3. For 42 workers from the night
According to the National Association of Homebuilders, the average life expectancies of a dishwasher and a microwave oven are about the same: 9 years. Assume that their finding was based on a sample of n1 = 60 dishwashers and n2 = 40 microwave ovens, and that the corresponding sample standard
In conducting her annual review of suppliers, a purchasing agent has collected data on a sample of orders from two of her company’s leading vendors. On average, the 24 shipments from company 1 have arrived 3.4 days after the order was placed, with a standard deviation of 0.4 days. The 30
A researcher has observed independent samples of females and males, recording how long each person took to complete his or her shopping at a local mall. The respective times, in minutes, are listed in file XR11072. Using the 0.025 level of significance in a one-tail test, would females appear to
For independent samples of customers of Internet providers A and B, the ages are as listed in file XR11073. Using the 0.05 level of significance in a nondirectional test, examine whether the variation in ages could be the same for customers of the two providers. A computer and statistical software.
An investment analyst has data for the past 8 years on each of two mutual funds, with the annual rates of return for each listed in file XR11074. On average, each fund has had an excellent annual rate of return over the time period for his data, but the analyst is concerned that a mutual fund with
Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $85, with a standard deviation of $28. Her friend John, taking the
The manufacturer of a small utility trailer is interested in comparing the amount of fuel used in towing the trailer with that required to overcome the weight and wind resistance of a rooftop carrier. Over a standard test route at highway speeds, 8 trips with the trailer resulted in an average fuel
A compressor manufacturer is testing two different designs for an air tank. Testing involves pumping air into a tank until it bursts, then noting the air pressure just prior to tank failure. Four tanks of design A are found to fail at an average of 1400 pounds per square inch (psi), with a standard
An industrial engineer has designed a new workstation layout that she claims will increase production efficiency. For a sample of 8 workers using the new workstation layout, the average number of units produced per hour is 36.4, with a standard deviation of 4.9. For a sample of 6 workers using the
Bob Techster is very serious about winning this year’s All-American Soap Box Derby competition. Since there is no wind-tunnel time available at the aerospace firm where his father works, Bob is using a local hill to test the effectiveness of an aerodynamic design change. In 10 runs with the
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