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business statistics a first course

Questions and Answers of Business Statistics A First Course

13.55 A random sample of 20 observations has been drawn from a normal population, and the sample variance is found to be s2 5 4.53. Determine the 95%confidence interval for 2.
13.54 A random sample of 10 observations has been drawn from a normal population, and the sample variance is found to be s2 5 19.5. Determine the 98%confidence interval for 2.
13.53 A random sample of 30 observations has been drawn from a normal population, and the sample variance is found to be s2 5 23.8. Determine the 95%confidence interval for 2.
13.52 In previous chapters, confidence intervals have been expressed in terms of a sample statistic plus or minus a given expression—e.g., }x 6 t(syÏwn ). However, the confidence interval for 2
13.51 In applying the chi-square statistic to estimation and tests for a population variance, why must the population be normally distributed?
13.50 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
13.49 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
13.48 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
13.47 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
13.46 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
13.45 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
13.44 For three independent samples, each with n 5 100, 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
13.43 For the following data obtained from four independent samples, use the 0.025 level in testing H0: 1 5 2 5 3 5 4 versus H1: At least one population proportion differs from the others.n1 5 150,
13.42 For the following data obtained from three independent samples, use the 0.05 level in testing H0: 1 5 2 5 3 versus H1: “At least one population proportion differs from the others.”n1 5 100,
13.41 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 5 low, 2 5 medium, 3 5
13.40 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
13.39 Collecting data for eight games, a basketball coach has compiled the following contingency table for the quarter of the game versus the result of “one-andone”free-throw attempts in which a
13.38 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
13.37 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
13.36 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
13.35 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
13.34 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
13.33 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,
13.32 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
13.31 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 thea. 5 0.025 level and df 5 5b.
13.30 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 thea. 5 0.05 level and df 5 3b. 5
13.29 For a contingency table with r rows and k columns, determine the df for the test ifa. r 5 3, k 5 4b. r 5 2, k 5 3c. r 5 4, k 5 5d. r 5 5, k 5 3e. r 5 3, k 5 7f. r 5 3, k 5 3
13.28 In carrying out a chi-square test for the independence of variables, what is the procedure for determining the number of degrees of freedom to be used in the test?
13.27 In conducting a chi-square test, why is it advisable that each expected frequency be at least 5.0? If the expected frequency in a cell happens to be less than 5.0, what should be done in order
13.26 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.
13.25 For Exercise 13.24, use the 0.05 level of significance in examining whether the data could have come from a normal distribution.
13.24 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
13.23 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
13.22 Approximately 13.2% of U.S. drivers are younger than age 25, with 37.7% in the 25–44 age group, and 49.1% in the 45-and-over category. For a random sample of 200 fatal accidents in her state,
13.21 Given the information in Exercise 13.20, use the 0.05 level in testing whether the number of defectives in each batch of n 5 25 could be binomially distributed with 5 0.1.
13.20 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
13.19 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 5 1.5.
13.18 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
13.17 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
13.16 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
13.15 Sample data have been collected, and the null hypothesis to be tested is H0: “The sample was drawn from a normal population in which 5 130.” If the analysis is based on a categorization
13.14 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
13.13 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
13.12 For the null hypothesis, H0: “The data were drawn from a Poisson distribution with 5 7.0,” how many degrees of freedom would be associated with the test if there are 8 cells in the table of
13.11 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?
13.10 In carrying out a chi-square goodness-of-fit test, what are the “k” and “m” terms in the “df 5 k 2 1 2 m”expression and why is each term present?
13.9 For df 5 15 and the constants A and B, identify the values of A and B such that the tail areas are equal anda. P(A , 2 , B) 5 0.80b. P(A , 2 , B) 5 0.90c. P(A , 2 , B) 5 0.95d. P(A , 2 , B) 5
13.8 For df 5 10 and the constants A and B, identify the values of A and B such that the tail areas are equal anda. P(A , 2 , B) 5 0.80b. P(A , 2 , B) 5 0.90c. P(A , 2 , B) 5 0.95d. P(A , 2 , B) 5
13.7 For df 5 8 and the constant A, identify the value of A such thata. P( 2 . A) 5 0.90b. P( 2 . A) 5 0.10c. P( 2 . A) 5 0.95d. P( 2 . A) 5 0.05e. P( 2 , A) 5 0.975f. P( 2 , A) 5 0.025
13.6 For df 5 5 and the constant A, identify the value of A such thata. P( 2 . A) 5 0.90b. P( 2 . A) 5 0.10c. P( 2 . A) 5 0.95d. P( 2 . A) 5 0.05e. P( 2 , A) 5 0.975f. P( 2 , A) 5 0.025
13.5 Why can the chi-square statistic never be negative?
13.4 Sketch the approximate shape of the chi-square curve when df 5 2 and when df 5 100.
13.3 In what way are the chi-square and normal distributions related?
13.2 Is the chi-square distribution a continuous distribution or a discrete distribution? Explain.
13.1 For what kinds of tests can chi-square analysis be used?
12.101 Three different point-of-purchase displays are being considered for lottery ticket sales at a chain of convenience stores. Two different locations within the store are also being considered.
12.100 Three different heat-treatment methods are being tested against four different zinc-coating techniques, with data representing the number of pounds required for a test probe to penetrate the
12.99 A magazine publisher is studying the influence of type style and darkness on the readability of her publication.Each of 12 persons has been randomly assigned to one of the cells in the
12.98 Interested in comparing the effectiveness of four different driving strategies, a government agency has equipped a compact car with a fuel- consumption meter that measures every 0.01 gal lon of
12.97 A state law enforcement agency has come up with three different methods for publicizing burglary-prevention measures during vacation periods.Recognizing that there are more burglaries in larger
12.96 Researchers have obtained and tested samples of four different brands of nylon rope that are advertised as having a breaking strength of 100 pounds. Given the breaking strengths (in pounds)
12.95 An investor has consulted four different financial advisors with regard to the expected annual rate of return for each of three portfolio possibilities she is considering. The financial
12.94 Four different alloy compositions have been used in manufacturing metal rods, with the hardness measurements shown here. Use the 0.05 level of significance in testing whether the population
12.93 A testing agency is evaluating three different brands of bathroom scales and has selected random samples of each brand. For brand A, a test object was found to weigh 204, 202, 197, 204, and 205
12.92 Given the following data from three in de pen dent samples, use the 0.025 level in determining whether the population means could be the same. (Use data file XR12092.) Sample 1 2 3 6 7 14 9 20
12.91 In an attempt to compare the assessments provided by the four assessors it employs, a municipal official sends each assessor to view the same five homes.Their visits to the homes are in a
12.90 Four different brands of brake shoes have been installed on 12 city transit buses, with each brand installed on 3 buses selected at random from the 12.The number of thousands of miles before
12.89 An industrial sales manager, testing the effectiveness of three different sales presentations, randomly selected a presentation to be used when making the next sales call on 14 customers. The
12.88 A firm that specializes in preparing recent law school graduates for the state bar exam has formulated two alternatives to their current preparation course. To examine the relative
Given the situation described in Exercise 12.85, suppose the groups are contrived so that each group contains one driver who is under 21 years of age, one driver who is between 22 and 60, and one
Given the situation described in Exercise 12.85, which ANOVA procedure from this chapter would be appropriate for the analysis of the resulting data?
Three different faceplate designs have been selected for the radio intended for a new luxury automobile, and safety engineers would like to examine the extent to which their operation will be
The personnel director for a large firm selects a random sample consisting of 100 clerical employees, then finds out whether they have been with the firm for more than 5 years and how many shares of
The data in an experiment have been examined using ANOVA, and a confidence interval has been constructed for the mean associated with each level for a factor. Which ANOVA technique (one-way,
Since the t-tests of Chapter 11 and the ANOVA techniques of this chapter are both involved with the comparison of sample means, why can’t the techniques always be used interchangeably?
Compare the respective purposes of one-way, randomized block, and two-way analysis of variance. In general, under what circumstances would each method be used?
Through separate calculations, verify the confidence interval for each of the factor-level means shown in the output for Exercise 12.79.
An experiment has been conducted to examine main and interactive effects of factor A (keyboard configuration, 3 levels) and factor B (word processing package, 2 levels). Each cell consists of two
For Exercise 12.77, and using the levels of the“shopping bag carried” factor as the horizontal axis and“seconds” as the vertical axis, plot and connect the cell means for the cells associated
Each of 12 undergraduate students has been randomly assigned to one of the 6 cells shown here. The purpose of the study is to test whether factor A (if a shopping bag is being carried) and factor B
For Exercise 12.75, and using the levels of the assembly method factor as the horizontal axis and “units produced” as the vertical axis, plot and connect the cell means for the cells associated
A study has been undertaken to examine the effect of background music and assembly method on the productivity of workers on a production line for electronic circuit boards. Each of 8 workers has been
Given the following summary table for a two-way ANOVA, fill in the missing items (indicated by asterisks), identify the sets of null and alternative hypotheses to be examined, then use the 0.05 level
Given the following data for a two-way ANOVA, identify the sets of null and alternative hypotheses, then use the 0.05 level in testing each null hypothesis. (Use data file XR12073.) Factor B 1 2 3 4
Given the following data for a two-way ANOVA, identify the sets of null and alternative hypotheses, then use the 0.05 level in testing each null hypothesis. (Use data file XR12072.) Factor B 1 2 3 1
Given the following data for a two-way ANOVA, identify the sets of null and alternative hypotheses, then use the 0.05 level in testing each null hypothesis. (Use data file XR12071.) Factor B 1 2 3 1
For a two-way ANOVA in which factor A operates on 3 levels and factor B operates on 4 levels, there are 2 replications within each cell. Given the following sum of squares terms, construct the
In a two-way ANOVA experiment, factor A is operating on 4 levels, factor B is operating on 3 levels, and there are 3 replications per cell. If MSAyMSE 5 3.54, MSByMSE 5 5.55, and MSAByMSE 5 12.40,
In a two-way ANOVA experiment, factor A is operating on 3 levels, factor B is operating on 2 levels, and there are 2 replications per cell. If MSAyMSE 5 5.35, MSByMSE 5 5.72, and MSAByMSE 5 6.75, and
12.66 In a two-way ANOVA experiment, factor A is operating on 4 levels, factor B is operating on 3 levels, and there are 3 replications per cell. How many treatments are there in this experiment?
In the two-way ANOVA, what is meant by the term replications?
What are main effects and interactive effects in the two-way ANOVA?
How is two-way ANOVA similar to the randomized block design? How does it differ?
Why are there more sets of null and alternative hypotheses that can be tested in two-way ANOVA compared to the one-way and randomized block designs?
What assumptions are required in using the twoway ANOVA?
What is the purpose of two-way analysis of variance?
Apply the dependent-samples t-test to the data in Exercise 12.53. Is the conclusion consistent with the one reached in that exercise? Explain.
Apply the dependent-samples t-test to the data in Exercise 12.49. Is the conclusion consistent with the one reached in that exercise? Explain.
Compare the randomized block ANOVA with two treatments to the dependent-samples t-test of Chapter 11.
The following Minitab output summarizes the results of a randomized block ANOVA in which the blocks consisted of 4 different income categories, the treatments were 3 different kinds of appeals for

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