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business statistics a first course
Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions
11.23 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
11.22 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
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 passengers recently processed by Fred, the mean processing time was 124.5 seconds, with a standard
In two independent samples, 2x 1 5 125.0, s1 5 21.5, n1 5 40, and 2x 2 5 116.4, s2 5 10.8, n2 5 35.Using the 0.025 level of significance, test H0: 1 # 2 versus H1: 1 . 2.
In two independent samples, 2x 1 5 165.0, s1 5 21.5, n1 5 40 and 2x 2 5 172.9, s2 5 31.3, n2 5 32.Using the 0.10 level of significance, test H0: 1 $ 2 versus H1: 1 , 2.
In two independent samples from populations that are normally distributed, 2x 1 5 35.0, s1 5 5.8, n1 5 12 and 2x 2 5 42.5, s2 5 9.3, n2 5 14. Using the 0.05 level of significance, test H0: 1 5 2 versus H1: 1 ? 2.
11.17 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
11.16 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
11.15 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
11.14 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.
11.13 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
11.12 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
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
11.10 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:8 boxes, 3.3, 6.4, 3.9, 5.4, new battery type: 5.1, 4.6, 4.9, 7.2 hrs 8
11.9 Media observers have been examining the number of minutes devoted to business and financial news during the half-hour evening news broadcasts of two local television channels. For each channel, they have randomly selected 10 weekday broadcasts and observed the number of minutes spent on
11.8 Sheila Smith, the manager of a large resort’s main hotel, has been receiving complaints from some guests that they are not being provided with prompt service upon approaching the front desk. In particular, she is concerned that desk staff might be providing female guests with less prompt
11.7 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
11.6 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
11.5 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
11.4 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
11.3 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
11.2 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
“When comparing two sample means, the t-test should be used only when the sample sizes are less than 30.” Comment.
Set the right and bottom sliders so that n 5 20 and 5 11.2. Now move the left slider upward and downward to change the level for the test. Observe the power of the test for each of the following values for : 0.01, 0.02, 0.05, 0.10, 0.20, 0.30, 0.40, and 0.50.
Set the left and bottom sliders so that 5 0.05 and 5 11.2. Now move the right slider upward and downward to change the sample size for the test. Observe the power of the test for each of the following values for n: 2, 10, 20, 40, 60, 80, and 100.
Set the left, right, and bottom sliders so that 5 0.05, n 5 15, and 5 the same value you selected in Applet Exercise 13.1. Now move the left slider upward and downward to change the level for the test. In what way(s) do these changes in affect the power of the test?
Using the left and right sliders, set up the test so that 5 0.10 and n 5 20. Now move the bottom slider so that the actual is as close as possible to 10 without being equal to 10 (e.g., 10.01). What is the value for the power of the test? Is this the value you would expect?
Using the slider, decrease the sample mean to approximately 1.310 minutes. Based on this confidence interval, would it seem believable that the true population mean might be 1.325 minutes?
Using the slider, increase the sample mean to approximately 1.330 minutes. What is the 95% confidence interval for ? Based on this confidence interval, would it seem believable that the true population mean might be 1.325 minutes?
When the applet initially loads, identify the sample mean and describe the 95% confidence interval for .Based on this confidence interval, would it seem believable that the true population mean might be 1.325 minutes?
If Springdale Mall offered exactly the same benefits as the other two shopping areas, we would expect exactly one-third of those who expressed an opinion to select it as the area best fitting the description for variable number 10 (“Easy to return/exchange goods”). In testing whether Springdale
Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis
In the past, the mean lifetime of diesel engine injection pumps has been 12,000 operating hours. A new injection pump is available that is promoted as lasting longer than the old version. In a test of 50 of the new pumps, the lifetimes are as listed in data file XR10113. Based on the sample data,
Use the decision rule associated with Exercise 10.111 and a range of selected assumed values for to construct the power curve for the test.
In making aluminum castings into alternator housings, an average of 3.5 ounces per casting must be trimmed off and recycled as a raw material.A new manufacturing procedure has been proposed to reduce the amount of aluminum that must be recycled in this way. For a sample of 35 castings made with the
Based on the sample results in Exercise 10.109, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion(0.25) within the interval? Given the presence or absence of the 0.25 value within the interval, is this consistent with the findings of
According to the U.S. Department of Justice, 25% of violent crimes involve the use of a weapon. We will assume that data file XR10109 contains a sample of the crime information for a given city, with data for the 400 crimes coded as 1 5 crime involved a weapon and 2 5 crime did not involve a
Before installing a high-tech laser exhibit near the exit area, a museum of American technology found the average contribution by patrons was $2.75 per person.For a sample of 30 patrons following installation of the new exhibit, the contributions are as listed in data file XR10108. Based on the
Historically, Shop-Mart has gotten an average of 2000 hours of use from its G&E fluorescent lightbulbs.Because its fixtures are attached to the ceiling, the bulbs are rather cumbersome to replace, and Shop-Mart is looking into the possibility of switching to Phipps bulbs, which cost the same. A
A consumer agency suspects that a pet food company may be underfilling packages for one of its brands. The package label states “1600 grams net weight,” and the president of the company claims the average weight is at least 1600 grams. For a simple random sample of 35 boxes collected by the
In an interview with a local newspaper, a respected trial lawyer claims that he wins at least 75% of his court cases. Bert, a skeptical statistics student, sets up a one-tail test at the 0.05 level of significance to evaluate the attorney’s claim. The student plans to examine a random sample of
A national chain of health clubs says the mean amount of weight lost by members during the past month was at least 5 pounds. Skeptical of this claim, a consumer advocate believes the chain’s assertion is an exaggeration.She interviews a random sample of 40 members, finding their mean weight loss
An exterminator claims that no more than 10%of the homes he treats have termite problems within 1 year after treatment. In a sample of 100 homes, local officials find that 14 had termites less than 1 year after being treated. At the 0.05 level of significance, evaluate the credibility of the
In a taste comparison test, it was found that 58 of 100 persons preferred the chunky version of a peanut butter over the creamy type. An interested observer would like to determine whether this proportion (0.58)is significantly greater than the (0.50) proportion that would tend to result from
The administrator of a local hospital has told the governing board that 30% of its emergency room patients are not really in need of emergency treatment (i.e., the problems could just as easily have been handled by an appointment with their family physician). In checking a random sample of 400
A 1931 issue of Time magazine contained an advertisement for Liberty magazine. According to a study cited by Liberty, it was found that 15% of Liberty families had a “mechanical refrigerator,” compared to just 8%for all U.S. families. Assuming that the study included a sample of 120 Liberty
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
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.
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
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
10.95 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
10.94 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
10.93 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
10.92 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
10.91 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
10.90 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
Plot the operating characteristic curve that corresponds to the power curve constructed for Exercise 10.86.
Plot the operating characteristic curve that corresponds to the power curve constructed for Exercise 10.84.
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
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 10.32.10.86 Using assumed true population percentages of 2%, 3%, 4%, 5%, 6%, and 7%, plot the power curve for the test in Exercise 10.63.
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.
For the test described in Exercise 10.32, assume that the true population mean for the new booklet is 5 2.80 hours. Under this assumption, what is the probability that the false null hypothesis, H0: $ 3.00 hours, will be rejected?
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 5 2.500 inches?
A hypothesis test has been set up and is to be con ducted at the 5 0.05 level of significance. If the sample size is doubled, what will be the effect on ?
What is an operating characteristic curve and how is it related to the power curve for a test?
What is a power curve and how is it applicable to hypothesis testing?
10.78 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
10.77 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
10.76 According to the National Collegiate Athletic Association (NCAA), 41% of male basketball players graduate within 6 years of enrolling in their college or university, compared to 56% for the student body as a whole. Assume that data file XR10076 shows the current status for a sample of 200
10.75 Based on the sample results in Exercise 10.74, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized proportion(0.80) within the interval? Given the presence or absence of the 0.80 value within the interval, is this consistent with the findings
10.74 It has been reported that 80% of taxpayers who are audited by the Internal Revenue Service end up paying more money in taxes. Assume that auditors are randomly assigned to cases, and that one of the ways the IRS oversees its auditors is to monitor the percentage of cases that result in the
10.73 Brad Davenport, a consumer reporter for a national cable TV channel, is working on a story evaluating generic food products and comparing them to their brand-name counterparts. According to Brad, consumers claim to like the brand-name products better than the generics, but they can’t even
10.72 Using the sample results in Exercise 10.71, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized population proportion (0.07) within the interval? Given the presence or absence of the 0.07 value within the interval, is this consistent with the
10.71 According to the U.S. Bureau of Labor Statistics, 7.0% of female hourly workers who are 16 to 24 years old are being paid minimum wage or less. (Note that some workers in some industries are exempt from the minimum wage requirement of the Fair Labor Standards Act and, thus, could be legally
10.70 Based on the sample results in Exercise 10.69, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion(0.55) within the interval? Given the presence or absence of the 0.55 value within the interval, is this consistent with the findings
10.68 Heritage Union has said that 66% of U.S. adults have purchased life insurance. Suppose that for a random sample of 50 adults from a given U.S. city, a researcher finds that only 56% of them have purchased life insurance.At the 0.05 level in a one-tail test, is this sample finding
10.67 In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Lately, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his or her first try. In a sample of 250
10.66 It has been claimed that 65% of homeowners would prefer to heat with electricity instead of gas. A study finds that 60% of 200 homeowners prefer electric heating to gas. In a two-tail test at the 0.05 level of significance, can we conclude that the percentage who prefer electric heating may
10.65 According to the human resources director of a plant, no more than 5% of employees hired in the past year have violated their preemployment agreement not to use any of five illegal drugs. The agreement specified that random urine checks could be carried out to ascertain compliance. In a
10.64 The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually apply for admission. In a sample of 300 persons to whom materials were sent, 30 students applied for admission. In a two-tail test at the 0.05 level of
10.63 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 no more than 2% of the items in the shipment are defective.Carry out an appropriate hypothesis test and comment on the credibility of
10.62 For a simple random sample, n 5 700 and p 5 0.63. At the 0.025 level, test H0: # 0.60 versus H1: . 0.60.
10.61 For a simple random sample, n 5 1000 and p 5 0.47. At the 0.05 level, test H0: $ 0.50 versus H1: , 0.50.
For a simple random sample, n 5 200 and p 5 0.34.At the 0.01 level, test H0: 5 0.40 versus H1: 0.40.
When carrying out a hypothesis test for a population proportion, under what conditions is it appropriate to use the normal distribution as an approximation to the (theoretically correct) binomial distribution?
10.58 Using the sample data in Exercise 10.57, construct and interpret the 95% confidence interval for the popula tion mean. Is the hypothesized population mean($817) within the interval? Given the presence or absence of the $817 value within the interval, is this consistent with the findings of
10.57 According to the Insurance Information Institute, the mean annual expenditure for automobile insurance for U.S. motorists is $817. Suppose that a government official in North Carolina has surveyed a simple random sample of 80 residents of her state, and that their auto insurance expenditures
10.56 The International Council of Shopping Centers reports that the average teenager spends $57 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and “teenappreciation days” that
10.55 Using the sample results in Exercise 10.54, construct and interpret the 90% confidence interval for the population mean. Is the hypothesized population mean(38 minutes) within the interval? Given the presence or absence of the 38 minutes value within the interval, is this consistent with the
10.54 The U.S. Census Bureau says the 52-question“long form” received by 1 in 6 households during the 2000 census takes a mean of 38 minutes to complete.Suppose a simple random sample of 35 persons is given the form, and their mean time to complete it is 36.8 minutes, with a standard deviation
10.53 Using the sample results in Exercise 10.52, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean(93 seconds) within the interval? Given the presence or absence of the 93 seconds value within the interval, is this consistent with the
10.52 In response to an inquiry from its national office, the manager of a local bank has stated that her bank’s average service time for a drive-through customer is 93 seconds. A student intern working at the bank happens to be taking a statistics course and is curious as to whether the true
10.51 It has been reported that the average life for halogen lightbulbs is 4000 hours. Learning of this figure, a plant manager would like to find out whether the vibration and temperature conditions that the facility’s bulbs encounter might be having an adverse effect on the service life of
10.50 Using the sample results in Exercise 10.49, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean($640,000) within the interval? Given the presence or absence of the $640,000 value within the interval, is this consistent with the
10.49 According to the Federal Reserve Board, the mean net worth of U.S. households headed by persons 75 years or older is $640,000. Suppose a simple random sample of 50 households in this age group is obtained from a certain region of the United States and is found to have a mean net worth of
10.48 During 2008, college work-study students earned a mean of $1478. Assume that a sample consisting of 45 of the work-study students at a large university was found to have earned a mean of $1503 during that year, with a standard deviation of $210. Would a one-tail test at the 0.05 level suggest
10.47 A scrap metal dealer claims that the mean of his cash sales is “no more than $80,” but an Inter nal Revenue Service agent believes the dealer is untruthful.Observing a sample of 20 cash customers, the agent finds the mean purchase to be $91, with a standard deviation of $21. Assuming the
10.46 The new director of a local YMCA has been told by his predecessors that the average member has belonged for 8.7 years. Examining a random sample of 15 membership files, he finds the mean length of membership to be 7.2 years, with a standard deviation of 2.5 years. Assuming the population is
10.45 Taxco, a firm specializing in the preparation of income tax returns, claims the mean refund for customers who received refunds last year was $150. For a random sample of 12 customers who received refunds last year, the mean amount was found to be $125, with a standard deviation of $43.
10.44 The International Coffee Association has reported the mean daily coffee consumption for U.S. residents as 1.65 cups. Assume that a sample of 38 people from a North Carolina city consumed a mean of 1.84 cups of coffee per day, with a standard deviation of 0.85 cups. In a two-tail test at the
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