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mathematics
statistics
Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions
For what kinds of tests can chi-square analysis be used?
In carrying out a chi-square goodness-of-fit test, what are the “k” and “m” terms in the “df = k – 1 – m” expression and why is each term present?
If a table of expected frequencies differs very little from the frequencies that were observed, would the calculated chi-square be large or small? Why?
For the null hypothesis, H0: “The data were drawn from a Poisson distribution with λ = 7.0,” how many degrees of freedom would be associated with the test if there are 8 cells in the table of frequencies to be analyzed?
For the null hypothesis, H0: “The data were drawn from a uniform continuous distribution,” how many degrees of freedom would be associated with the test if there are 5 cells in the table of frequencies to be analyzed?
Sample data have been collected, and the null hypothesis to be tested is, H0: “The sample was drawn from a normal population.” If the analysis is based on a categorization that includes 5 cells: a. How many degrees of freedom will be associated with the test? b. For a test at the 0.05 level,
Sample data have been collected, and the null hypothesis to be tested is H0: “The sample was drawn from a normal population in which μ = 130.” If the analysis is based on a categorization that includes 8 cells: a. How many degrees of freedom will be associated with the test? b. For a test at
According to the Bureau of the Census, 18.1% of the U.S. population lives in the Northeast, 21.9% in the Midwest, 36.7% in the South, and 23.3% in the West. In a random sample of 200 recent calls to a national 800-number hotline, 39 of the calls were from the Northeast, 55 from the Midwest, 60 from
From the one-day work absences during the past year, the personnel director for a large firm has identified the day of the week for a random sample of 150 of the absences. Given the following observed frequencies, and for α = 0.01, can the director conclude that one-day absences
It has been reported that 8.7% of U.S. households do not own a vehicle, with 33.1% owning 1 vehicle, 38.1% owning 2 vehicles, and 20.1% owning 3 or more vehicles. The data for a random sample of 100 households in a resort community are summarized in the frequency distribution below. At the 0.05
For the data provided in Exercise 13.18, use the 0.05 level in testing whether the sample could have been drawn from a Poisson population with λ = 1.5.In exercise
Employees in a production department assemble the products, then submit them in batches of 25 for quality inspection. The number of defectives in each batch of a random sample of 50 recently produced batches is shown below. At the 0.01 level, test whether the population of x = the number of
Given the information in Exercise 13.20, use the 0.05 level in testing whether the number of defectives in each batch of n = 25 could be binomially distributed with π = 0.1.In exercise
Approximately 13.2% of U.S. drivers are younger than age 25, with 37.7% in the 25–44 age group, and49.1% in the 45-and-over category. For a random sample of 200 fatal accidents in her state, a safety expert finds that 42 drivers were under 25 years old, 80 were25–44 years old, and 78 were at
For a random sample of 200 U.S. motorists, the mileages driven last year are in data file XR13023. Use the 0.01 level of significance in determining whether the mileages driven by the population of U.S. motorists could be normally distributed.
For the previous 300 plywood panels from a lumber company’s production line, the data in file XR13024 list the number of surface defects per panel. Based on this information, use the 0.05 level of significance in examining whether the data could have come from a Poisson distribution.
For Exercise 13.24, use the 0.05 level of significance in examining whether the data could have come from a normal distribution. In exercise For the previous 300 plywood panels from a lumber company’s production line, the data in file XR13024 list the number of surface defects per panel. Based on
The outstanding balances for 500 credit-card customers are listed in file XR13026. Using the 0.10 level of significance, examine whether the data could have come from a normal distribution.
For a contingency table with r rows and k columns, determine the df for the test if a. r = 3, k = 4 b. r = 2, k = 3 c. r = 4, k = 5 d. r = 5, k = 3 e. r = 3, k = 7 f. r = 3, k = 3
In testing the independence of two variables described in a contingency table, determine the critical value of chi-square if the test is to be conducted at the a. α = 0.05 level and df = 3 b. α = 0.01 level and df = 5 c. α = 0.10 level and df = 2 d. α = 0.025 level and df = 4
In testing the independence of two variables described in a contingency table, determine the critical value of chi-square if the test is to be conducted at the a. α = 0.025 level and df = 5 b. α = 0.05 level and df = 8 c. α = 0.01 level and df = 6 d. α = 0.10 level and df = 4
In a test of the independence of two variables, one of the variables has two possible categories and the other has three possible categories. What will be the critical value of chi-square if the test is to be carried out at the 0.025 level? At the 0.05 level?
A researcher has observed 100 shoppers from three different age groups entering a large discount store and noted the nature of the greeting received by the shopper. Given the results shown here, and using the 0.025 level of significance, can we conclude that the age category of the shopper is
A research organization has collected the following data on household size and telephone ownership for 200 U.S. households. At the 0.05 level, are the two variables independent? Based on the chi-square table, what is the most accurate statement that can be made about the p-value for the test?
Researchers in a California community have asked a sample of 175 automobile owners to select their favorite from three popular automotive magazines. Of the 111 import owners in the sample, 54 selected Car and Driver, 25 selected Motor Trend, and 32 selected Road & Track. Of the 64 domestic-make
A pharmaceutical firm, studying the selection of “name brand” versus “generic equivalent” on prescription forms, has been given a sample of 150 recent prescriptions submitted to a local pharmacy. Of the 44 under-40 patients in the sample, 16 submitted a prescription form with the “generic
Customers of the Sky Mountain Grocery chain are routinely asked at the checkout whether they prefer paper or plastic bags for their purchases. In a recent study, researchers observed the type of bag specified and surveyed the customer for other information, including his or her level of education.
Upon leaving an assembly area, production items are examined and some of them are found to be in need of either further work or total scrapping. Tags on a sample of 150 items that failed final inspection show both the recommended action and the identity of the inspector who examined the item. The
Collecting data for eight games, a basketball coach has compiled the following contingency table for the quarter of the game versus the result of €œone-and one€ free-throw attempts in which a second shot can be attempted if the first one is made. At the 0.025 level, can he
The manager of a television station employs three different weather reporters (coded as 1–3) and has surveyed viewers to find out whether education level (coded as 1–4) might be related to the weather reporter the viewer prefers. For the results listed in data file XR13040, use the 0.05 level
For a random sample of returns audited by the IRS, the data in file XR13041 describe the results according to the income category of the audited party (coded as 1 – low, 2 = medium, 3 = moderate, and 4 = high) and the type of IRS personnel who examined the return (coded as 1 = revenue agent, 2 =
For the following data obtained from three independent samples, use the 0.05 level in testing H0: π1 = π2 = π3 versus H1: “At least one population proportion differs from the others.” n1 = 100, p1 = 0.20 n2 = 120, p2 = 0.25 n3 = 200, p3 = 0.18
For the following data obtained from four independent samples, use the 0.025 level in testing H0: π1 = π2 = π3 = π4 versus H1: At least one population proportion differs from the others. n1 = 150, p1 = 0.30 n2 = 80, p2 = 0.20 n3 = 140, p3 = 0.25 n4 = 50, p4 = 0.26
For three independent samples, each with n = 100, the respective sample proportions are 0.30, 0.35, and 0.25. Use the 0.05 level in testing whether the three population proportions could be the same.
An investment firm survey included the finding that 52% of 150 clients describing themselves as “very aggressive” investors said they were optimistic about the near-term future of the stock market, compared to 46% of 100 describing themselves as “moderate” and 38% of 100 describing
According to a study by the Pew Research Center, 75% of adults 18–30 said they went online daily, compared with 40% of those 65–74, and just 16% for those 75 or older. Using the 0.01 level of significance, and assuming that a random sample of 200 persons was surveyed from each age group, could
It has been reported that 18.3% of all U.S. households were heated by electricity in 1980, compared to 27.4% in 1995 and 31.5% in 2005. At the 0.05 level, and assuming a sample size of 1000 U.S. households for each year, test whether the population percentages could be equal for these years.
In analyzing the consumption of cottage cheese by members of various occupational groups, the United Dairy Industry Association found that 326 of 837 professionals seldom or never ate cottage cheese, versus 220 of 489 white- collar workers and 522 of 1243 blue-collar workers. Assuming independent
The movie complex at a shopping mall shows three movies simultaneously on the same evening. On a recent Friday evening, each movie drew a capacity crowd. A sample of the evening’s movie patrons have been coded according to whether they purchased snacks (1 = pur chased snacks, 2 = did not purchase
An experiment has been conducted to compare the ease of use of several pocket calculators, with subjects randomly provided with one of four calculator designs. The subjects have been coded according to which one of the four calculators they tried (codes = 1–4) and whether they thought the
A random sample of 30 observations has been drawn from a normal population, and the sample variance is found to be s2 = 23.8. Determine the 95% confidence interval for σ2.
A random sample of 10 observations has been drawn from a normal population, and the sample variance is found to be s2 = 19.5. Determine the 98% confidence interval for σ2.
A random sample of 20 observations has been drawn from a normal population, and the sample variance is found to be s2 = 4.53. Determine the 95% confidence interval for σ2.
A pharmaceutical company has specified that the variation in the quantity of active ingredient in its leading prescription medication must be such that the population standard deviation must be no more than 1.20 micrograms. The ingredient content of the pills is normally distributed. In a random
During the early stages of production for a single-cylinder engine designed for use in portable generators, the manufacturer randomly selects 12 engines from the end of the assembly line and subjects them to a battery of tests. In the horsepower tests, the engines are found to have an output
An instrument maker has randomly selected and submitted 20 of its electronic blood- pressure measurement units to a medical laboratory for testing. At the lab, each unit measures the “blood pressure” of a testing device that simulates a human arm; within the device the pressure is a known
A random sample of n 5 30 is drawn from a population that is normally distributed, and the sample variance is s2 = 41.5. Use α = 0.05 in testing H0: σ2 = 29.0 versus H1: σ2 ≠ 29.0.
For df = 5 and the constant A, identify the value of A such that a. P(x2 > A) = 0.90 b. P(x2 > A) = 0.10 c. P(x2 > A) = 0.95 d. P(x2 > A) = 0.05 e. P(x2 < A) = 0.975 f. P(x2 < A) = 0.025
A random sample of n = 12 is drawn from a population that is normally distributed, and the sample variance is s2 = 19.3. Use α = 0.025 in testing H0: σ2 ≤ 9.4 versus H1: σ2. 9.4.
According to industry specifications, the standard deviation of gasket thicknesses for a given application must be no more than 3 thousandths of an inch. In a random sample of 25 gaskets produced by one of the firms, the sample standard deviation is found to be 3.7 thousandths of an inch. Assuming
In past studies, a fast-food franchise has found the standard deviation of weights for quarter-pound hamburgers to be approximately 0.28 ounces after cooking. A consultant has suggested a new procedure for hamburger preparation and cooking that she believes will reduce the variability in the cooked
Given the information in Exercise 13.62 and data file XR13062, determine the 98% confidence interval for the population variance of the cooked weights for hamburgers prepared using the consultant’s recommended cooking procedure. In exercise In past studies, a fast-food franchise has found the
The personnel director of a large firm has summarized a random sample of last year€™s absentee reports in the accompanying contingency table. At the 0.01 level of significance, test the independence of age versus length of absence.
Frank Gerbel, a local insurance representative, has hired a part-time assistant to make €œcold€ calls on potential customers. The assistant has been given a quota of 20 such calls to make each day, and a call is deemed a success if the potential customer agrees to set up an
For the most recent year reported, the Federal Bureau of Investigation has listed the following data for robberies in the United States.The police chief in a medium-sized community has data indicating that the respective numbers of these robberies in his community during the same year were 23, 9,
The following data are the number of persons who were waiting in line at a checkout counter at 100 randomly selected times during the week. At the 0.05 level, test whether the population of these values could be Poisson distributed.
A newspaper reporter, collecting data for a feature article on her state lottery system, has found the 200 digits most recently selected to be distributed as shown below. Based on this information, and using the 0.10 level of significance, can she conclude that the digits have not been drawn from
According to the Bureau of the Census, the U.S. population includes 37.7 million persons who were born in Europe, Asia, the Caribbean, Central America, South America, or in another area outside the United States. A percentage breakdown of the regions of birth is shown here. If a random sample of
For df = 8 and the constant A, identify the value of A such that a. P(x2 > A) = 0.90 b. P(x2 > A) = 0.10 c. P(x2 > A) = 0.95 d. P(x2 > A) = 0.05 e. P(x2 < A) = 0.975 f. P(x2 < A) = 0.025
A national public television network has found that 35% of its contributions are for less than $20, with 45% for $20–$50, and 20% for more than $50. In a random sample of 200 of the contributions to a local station, 42% were for less than $20, 43% were for $20–$50, and 15% were over $50. At the
Twenty-five percent of the employees of a large firm have been with the firm less than 10 years, 40% have been with the firm for 10 to 20 years, and 35% have been with the firm for more than 20 years. Management claims to have randomly selected 20 employees to participate in a drawing for a new
The following contingency table describes types of collisions versus driving environments for a random sample of two-vehicle accidents that occurred in a given region last year. At the 0.01 level of significance, can we conclude that the type of collision is independent of whether the accident took
Of the students at a large university, 30% are freshmen, 25% are sophomores, 25% are juniors, and 20% are seniors. The representation of the four classes in the 100-member marching band is found to be 24%, 28%, 19%, and 29%. At the 0.05 level of significance, does the composition of the marching
Three different instructional techniques are being considered for training mechanics to perform a difficult emissions-reduction adjustment on fuel-injection engines. Each of 60 mechanics is randomly assigned to receive one of the training techniques. For the 20 trained by technique A, 70% are able
Taking air samples at random times during a 2-month period, an environmental group finds the standard deviation of ozone concentration measurements in the vicinity of a chemical plant to be 0.03 parts per million (ppm). The group believes the population of ozone measurements is normally
A local bank has recently installed an automatic teller machine (ATM). At a regional meeting, an ATM specialist tells the bank manager that usage times will be normally distributed and the variability in the amount of time customers require to use the machine will start out relatively high, then
According to the Bureau of the Census, 36% of U.S. adults in the $20,001€“$35,000 income group participated in adult education during the most recent reporting year. Data for this and other groups are shown here.Assuming independent samples of 1000 for each of these income groups, use the
Over the past year, an audio store has sold stereo systems produced by three different manufacturers. Of the 400 units from company A, 12% were returned for service during the warranty period. This compares to 15% of 300 units from company B, and 16% of 500 from company C. Assuming that the
Union members in a large firm work in three departments: assembly, maintenance, and shipping/ receiving. Twenty of a random sample of 30 assembly workers say they intend to ratify the new contract negotiated by union leaders and management. This compares to 30 of 40 maintenance workers and 25 of 50
For df = 10 and the constants A and B, identify the values of A and B such that the tail areas are equal and a. P (A < x2 < B) = 0.80 b. P (A < x2 < B) = 0.90 c. P (A < x2 < B) = 0.95 d. P (A < x2 < B) = 0.98
An aspirin manufacturer has designed the childproof cap on its bottles so that it must be pressed down before it can be turned and removed. A consumer magazine has randomly purchased 15 bottles of the company’s aspirin for analysis in a feature article on pain relievers and their packaging. Among
A campus newspaper is examining the extent to which various segments of the university community favor the Student Government Association’s recommendation that the school make the transition from Division II to Division I NCAA football. A random sample of 100 students is chosen from each of the
A casting machine is supposed to produce units for which the standard deviation of weights is 0.4 ounces. According to the maker of the machine, it should be shut down and thoroughly examined for wear if the standard deviation becomes greater than the 0.4 ounces that has been specified. In a random
At the beginning of last year, a power company asked each of its industrial customers to estimate how much electricity it would require during the year. At the end of the year, the power company recorded the extent to which a customer’s estimate was over or under the amount of electricity
The data in file XR13084 represent the Scholastic Aptitude Test (SAT) scores for a random sample of 200 high school seniors who have taken the exam. Using the 0.025 level of significance, test whether the sample scores could have come from a population that is normally distributed. A computer and
For a random sample of households in a county, file XR13085 lists the number of TV sets owned by each of the households in the study. Using the 0.025 level of significance, test whether x = the number of television sets per household could be Poisson distributed in the county’s households. A
Researchers have coded a random sample of households according to household income (1 = under $30,000, 2 = $30,000–$49,999, 3 = $50,000–$69,999, and 4 = $70,000 or more) and number of vehicles owned (1 = 0, 2 = 1 or 2, and 3 = 3 or more). The data are in file XR13086. Using the 0.05 level of
Safety researchers in a government agency believe that too much variability in the speeds of vehicles on urban sections of interstate highways can contribute to accidents by causing a greater level of interaction between vehicles traveling in the same direction. They believe that a standard
Given the information in Exercise 13.87 and data file XR13087, determine the 95% confidence interval for the population variance of the speeds of vehicles passing this location on the urban interstate. In exercise Safety researchers in a government agency believe that too much variability in the
For df = 15 and the constants A and B, identify the values of A and B such that the tail areas are equal and a. P(A < x2 < B) = 0.80 b. P(A < x2 < B) = 0.90 c. P(A < x2 < B) = 0.95 d. P(A < x2 < B) = 0.98
Ted Thorndike is trying to close a sale with the Alvindale Chipmunks, a minor-league professional baseball team. Although his grandfather isn’t very thrilled about any kind of deal with somebody with a name like “Chipmunks,” Ted feels this could mark the beginning of some really high-level
Part I: Respondent Characteristics and the Area Judged Best for Bargains 1. Construct and use the 0.05 level in testing the contingency table for variables 26 and 17. Can we conclude that the gender of the respondent is independent of the shopping area judged best for bargains? 2. Repeat step 1 for
In the Baldwin Computer Sales case, visited previously in Chapters 3 and 5, one of the areas of concern regarding the student purchase program was whether defaulting on the computer payments is independent of the university attended by the student. Using the BALDWIN data file, apply the appropriate
The placement director for a university claims that last year’s graduates had a median starting salary of $35,000. For a random sample of graduates, the starting salaries, in thousands of dollars, are listed in data file XR14010. At the 0.05 level, could the director’s claim be true? Identify
The median age for a male at the time of his first marriage has been reported as 27.5 years. In a given region, a random sample of males’ first marriages showed the ages listed in data file XR14011. Using the 0.05 level of significance, test whether the median age at which males in this region
What is the parametric counterpart to the Wilcoxon signed rank test for paired samples? Compare the assumptions involved in using the respective tests.
For nine paired samples, the data are as listed in the table. For d = the difference between paired observations (x1 €“ x2), use the 0.10 level of significance in testing H0: md ‰¤ 0 versus H1: md > 0.
For ten paired samples, the data are as listed here. For d = the difference between paired observations (x1 €“ x2), use the 0.10 level of significance in testing H0: md = 0 versus H1: md ‰ 0.
Tom Frederick is the computer support manager for a large company whose employees have been complaining about €œspam,€ which many of us know as unwanted e-mail to solicit our money or our attention. Tom asked a sample of 9 employees to keep track of the number of spam messages
A researcher studying the purchase habits of eight married couples has found they spent the amounts shown below for clothing. At the 0.05 level, can we conclude that the population of husbands and wives do not spend equally in this purchase category?
A new procedure is being tested for the assembly of electronic circuit boards. For each of five employees, the time required to assemble a board is measured for both the current procedure and the method that has been proposed. Given the times listed in the table, use the 0.025 level of significance
Early in the 1995–1996 NHL hockey season, players and coaches observed with great interest an apparent drop in the number of goals scored so far during that season, compared to scoring over the same number of games during the previous season. For each team, the number of goals in the 1995–1996
A company has randomly selected a number of employees to test the effectiveness of a speed-reading course. If the course is found to significantly increase reading speed, it will be offered to all of the firm’s clerical employees. For each of the employees selected for the test, reading speeds
What are some advantages and disadvantages of nonparametric testing?
Differentiate between the Kruskal-Wallis test and the one-way analysis of variance in terms of their assumptions and the circumstances under which each should be applied.
For the following independent and random samples, use the 0.05 level of significance in testing whether the population medians could be equal.
For the following independent and random samples, use the 0.10 level of significance in testing whether the population medians could be equal.
In general, when should a nonparametric technique be used instead of its parametric counterpart?
A sample of five law firms has been selected from each of three major cities for the purpose of obtaining a quote for legal services on a relatively routine business contract. The quotes provided by the fifteen firms are as shown in the accompanying table. At the 0.05 level of significance, does it
In testing three different rubber compounds, a tire manufacturer finds the tread life of tires made from each to be as shown below. At the 0.05 level, could the three compounds deliver the same median tread life?
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