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business statistics a first course

Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions

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, a safety expert finds that 42 drivers were under 25 years old, 80 were 25–44 years old, and 78
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 produced batches is shown below. At the 0.01 level, test whether the population of x 5 the number of
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 of 100 households in a resort community are summarized in the frequency distribution below. At the
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 observed frequencies, and for 5 0.01, can the director conclude that one-day absences during the
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 to a national 800-number hotline, 39 of the calls were from the Northeast, 55 from the Midwest, 60
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 that includes 8 cells:a. How many degrees of freedom will be associated with the test?b. For a test
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 cells:a. How many degrees of freedom will be associated with the test?b. For a test at the 0.05
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 frequencies to be analyzed?
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 frequencies to be analyzed?
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 0.98
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 0.98
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. Eighteen stores for which lottery ticket sales have been comparable are randomly assigned to the six
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 layer of zinc coating. Metal samples have been randomly assigned to the factor levels, with two
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 experiment, and the data are the number of seconds each person requires to read a brief test item. For these
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 gasoline consumed.Each of five randomly selected drivers applies each strategy in negotiating the
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 communities than in smaller communities, three communities have been randomly selected from each
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) shown here, use the 0.025 level in comparing the brands. (Use data file XR12096.) Brand A Brand B Brand
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 advisors have been chosen because they are known to range from very conservative(advisor A) to very
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 means might be equal, then construct the 95% confidence interval for each population mean. (Use data
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 pounds on the five scales sampled. For four scales of brand B, the test object weighed 201, 199,
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 18 18 11 23 12 15 17 13 23 27 27 10 16
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 random order, and the assessments they provide are as shown here. Use the 0.025 level in comparing the
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 the lining required replacement was as follows for each bus.(Use data file XR12090.)a. From the
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 numbers of units purchased as a result of each sales call are shown here. Use the 0.05 level in
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 effectiveness of the three possible courses, they have set up a study in which they randomly assigned a group of
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 driver who is over 60. If the three groups were constructed in this manner, would the ANOVA procedure
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 relatively intuitive to the motorist. Nine drivers are selected and randomly placed into one of three
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 company’s stock they own. The purpose is to see if longevity within the firm has an influence
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, randomized block, or two-way) has not been used in this analysis?Explain.
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 replications, representing the number of minutes each of two secretaries randomly assigned to that cell
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 with the “sloppy” level of the dress factor. On the same graph, plot and connect the cell means
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 (mode of dress) have main and interactive effects regarding the number of seconds it takes to get
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 with the “classical music”level of the background music factor. On the same graph, plot and
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 randomly assigned to one of 4 cells, as shown here. So that each worker will hear only the intended
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 in reaching a conclusion regarding each null hypothesis. Degrees Variation Source Sum of of Mean
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 1 58 63 64 66 64 66 68 68 61 61 59 72 Factor A 2 59 56 58 60 64 61 60 59 59 56 63 62 3 64 57 55 61
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 1 152 158 160 151 154 160 Factor A 2 158 164 152 154 158 155 3 160 147 147 161 150 146
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 13 19 19 10 15 17 Factor A 2 15 15 55 22 16 19 17 67
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 appropriate table of ANOVA summary findings and use the 0.05 level in examining the null and alternative
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, and using the 0.025 level of significance, what conclusions would be reached regarding the respective
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 using the 0.05 level of significance, what conclusions would be reached regarding the respective
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? Explain.12.67 For the two-way ANOVA model, xijk5 1 i 1j 1 ()ij 1 ijk, explain the meaning of
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 contributions to a national charity, and the variable measured(dollars) was the amount contributed to
12.55 Given the following summary table for a randomized block design, fill in the missing items (indicated by asterisks), identify the null and alternative hypotheses in terms of the treatment effects, then use the 0.05 level of significance in reaching a conclusion regarding the null hypothesis.
12.54 Given the following summary table for a randomized block design, fill in the missing items (indicated by asterisks), identify the null and alternative hypotheses in terms of the treatment effects, then use the 0.025 level of significance in reaching a conclusion regarding the null hypothesis.
12.53 Two different machine control-button configurations are being tested. Recognizing that some operators are faster than others, management uses seven operators as blocks, then has each operator carry out a standard operation using each control-button layout. Each operator proceeds from one
12.52 Three racquetball players, one from each skill level, have been randomly selected from the membership list of a health club. Using the same ball, each person hits five serves, one with each of five racquets, and using the racquets in a random order. Each serve is clocked with a radar gun, and
12.51 The continuous operating lifetime of a battery depends very much on the electrical demands of the device in which the battery is installed. In a test of three battery brands, four examples of each brand are randomly selected. Three examples of four different toys are also randomly selected,
12.50 A randomized block design has five different age groups as blocks, and members of each block have been randomly assigned to the treatment groups shown here.For these data, use the 0.05 level in determining whether the treatment effects could all be zero. Using the 0.01 level, evaluate the
12.49 A randomized block design has three different income groups as blocks, and members of each block have been randomly assigned to the treatment groups shown here. For these data, use the 0.01 level in determining whether the treatment effects could both be zero.Using the 0.01 level, evaluate
12.48 For a randomized block experiment having three treatments and three blocks, the results include the following sum of squares terms. Based on this information, construct the appropriate table of ANOVA summary findings and use the 0.05 level of significance in testing whether all of the
12.47 For a randomized block experiment in which there are five treatments and four blocks, the calculated value of F 5 MSTRyMSE is 3.75. Using the 0.05 level of significance, what conclusion would be reached? Based on the F distribution tables, what is the most accurate statement that could be
12.46 For a randomized block experiment in which there are three treatments and two blocks, the calculated value of F 5 MSTRyMSE is 16.1. Using the 0.05 level of significance, what conclusion would be reached? Based on the F distribution tables, what is the most accurate statement that could be
12.45 In one-way ANOVA, we were able to determine the confidence interval for the population value of each treatment mean. Why is this not appropriate for the treatments being examined in the randomized block design?
In the randomized block design, what benefit is gained from blocking?
For the randomized block ANOVA model, xij 5 1 j 1 i 1 ij, explain the meaning of each term in the equation, then use the appropriate terms from the equation in presenting and explaining the possible sets of null and alternative hypotheses that can be tested.
How does the randomized block design differ from the one-way, completely randomized design?
What assumptions are required in using the randomized block design?
What is the purpose of the randomized block design?
12.39 Use the pooled-variances t-test of Chapter 11 in comparing the sample means for the data of Exercise 12.30. Is the conclusion consistent with the one reached in that exercise? Explain.
12.38 Use the pooled-variances t-test of Chapter 11 in comparing the sample means for the data of Exercise 12.28. Is the conclusion consistent with the one reached in that exercise? Explain.
In general, how do the assumptions, procedures, and results of one-way ANOVA compare with those for the pooled-variances t-test of Chapter 11?
Given the summary information in Exercise 12.34, verify the calculation of the 95% confidence interval for each of the treatment means.
Given the summary information in Exercise 12.33, verify the calculation of the 95% confidence interval for each of the treatment means.
A large investment firm claims that no discrepancy exists between the average incomes of its male and female investment counselors. Random samples consisting of 15 male counselors and 17 female counselors have been selected, and the results examined through the use of ANOVA. In terms of this
12.33 A researcher has used a standard test in measuring the job-satisfaction scores for employees randomly selected from three departments of a large firm. Interpret the results summarized in the following Minitab output. Analysis of Variance Source DF SS MS Factor 2 69.9 35.0 F 2.45 p 0.092 Error
12.32 For the following summary table for a one-way ANOVA, fill in the missing items (indicated by asterisks), identify the null and alternative hypotheses, then use the 0.025 level of significance in reaching a conclusion regarding the null hypothesis. Degrees of Freedom Mean Square F 665.0 4 ***
12.31 For the following summary table for a one-way ANOVA, fill in the missing items (indicated by asterisks), identify the null and alternative hypotheses, then use the 0.05 level of significance in reaching a conclusion regarding the null hypothesis. Variation Source Sum of Squares Degrees of
12.30 Safety researchers, interested in determining whether the occupancy of a vehicle might be related to the speed at which the vehicle is driven, have observed the following speed (mph) measurements for two random samples of vehicles. (Use data file XR12030.)a. What are the null and alternative
12.29 Each of fifteen 60-watt lightbulbs has been randomly placed into an outlet for which the voltage is 3 volts below the line voltage, 2 volts below the line voltage, or equal to the line voltage. The following data are the lifetimes of the bulbs, expressed in days of continuous use. (Use data
12.28 Students in a large section of a biology class have been randomly assigned to one of two graduate students for the laboratory portion of the class. A random sample of final examination scores has been selected from students supervised by each graduate student, with the following results. (Use
12.27 A study has been carried out to compare the United Way contributions made by clerical workers from three local corporations. A sample of clerical workers has been randomly selected from each firm, and the dollar amounts of their contributions are as follows. (Use data file XR12027.)a. What
12.26 For the following data from independent samples, could the null hypothesis that the population means are equal be rejected at the 0.05 level? (Use data file XR12026.) Sample 1 15.2 Sample 2 Sample 3 Sample 4 10.2 14.9 11.5 12.2 12.1 13.0 13.1 15.0 8.5 10.8 11.5 14.6 8.1 10.7 6.3 9.7 10.9 13.3
12.25 For the experiment described in Exercise 12.8, what null and alternative hypotheses would be appropriate for the one-way ANOVA to examine the data? If the data are as shown here, what conclusion would be reached at the 0.01 level of significance? (Use data file XR12025.) Breaking Strengths
12.24 For the experiment described in Exercise 12.7, what null and alternative hypotheses would be appropriate for the one-way ANOVA to examine the data? If the data are as shown here, what conclusion would be reached at the 0.025 level of significance? From the F distribution tables, what is the
12.23 For the experiment described in Exercise 12.6, what null and alternative hypotheses would be appropriate for the one-way ANOVA to examine the data? Given the following data, what conclusion would be reached at the 0.05 level of significance? From the F distribution tables, what is the

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