Consider the valve opening data displayed in Table 11.1. Suppose the data represent valves produced on four different machines on three different shifts and that the quality controllers want to know whether there is any difference in the mean measurements of valve openings by shift or by machine. The data are given here, organized by machine and shift. In addition, Excel has been used to analyze the data with a two-way ANOVA. What are the hypotheses for this problem? Study the output in terms of significant differences. Discuss the results obtained. What conclusions might the quality controllers reach from this analysis?
Table 11.1:
Valve Opening Measurements (in cm) for 24 Valves Produced on an Assembly Line
> A bank officer wants to determine the amount of the average total monthly deposits per customer at the bank. He believes an estimate of this average amount using a confidence interval is sufficient. How large a sample should he take to be within $200 of
> Determine the sample size necessary to estimate p for the following information. a) E = .02, p is approximately .40, and confidence level is 96% b) E is to be within .04, p is unknown, and confidence level is 95% c) E is to be within 5%, p is approximate
> Determine the sample size necessary to estimate μ for the following information. a) σ = 36 and E = 5 at 95% confidence b) σ = 4.13 and E = 1 at 99% confidence c) Values range from 80 to 500, error is to be within 10, and the confidence level is 90% d) Va
> Suppose a random sample of 14 people 30–39 years of age produced the household incomes shown here. Use these data to determine a point estimate for the population variance of household incomes for people 30–39 years of
> A manufacturing plant produces steel rods. During one production run of 20,000 such rods, the specifications called for rods that were 46 centimeters in length and 3.8 centimeters in width. Fifteen of these rods comprising a random sample were measured f
> The Interstate Conference of Employment Security Agencies says the average workweek in the United States is down to only 35 hours, largely because of a rise in part-time workers. Suppose this figure was obtained from a random sample of 20 workers and tha
> Use the following sample data to estimate the population variance. Produce a point estimate and a 98% confidence interval. Assume the data come from a normally distributed population.
> For each of the following sample results, construct the requested confidence interval. Assume the data come from normally distributed populations. a) n = 12, x̅ = 28.4, s2 = 44.9; 99% confidence for σ2 b) n = 7, x̅ = 4.37, s = 1.24; 95% confidence for σ2
> Suppose a survey of 275 executives is taken in an effort to determine what qualities are most important for an effective CEO to possess. The survey participants are offered several qualities as options, one of which is “communication.” One hundred twenty
> A small lawnmower company produced 1500 lawnmowers in 2008. In an effort to determine how maintenance-free these units were, the company decided to conduct a multiyear study of the 2008 lawnmowers. A sample of 200 owners of these lawnmowers was drawn ran
> A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4. What is the point estimate of μ? Construct a 94% confidence interval for μ.
> A random sample of 81 items is taken, producing a sample mean of 47. The population standard deviation is 5.89. Construct a 90% confidence interval to estimate the population mean.
> According to Runzheimer International, in a survey of relocation administrators 63% of all workers who rejected relocation offers did so for family considerations. Suppose this figure was obtained by using a random sample of the files of 672 workers who
> For a random sample of 36 items and a sample mean of 211, compute a 95% confidence interval for μ if the population standard deviation is 23.
> Use the following information to construct the confidence intervals specified to estimate μ. a) 95% confidence for x̅ = 25, σ = 3.5, and n = 60 b) 98% confidence for x̅ = 119.6, σ = 23.89, and n = 75 c) 90% confidence for x̅ = 3.419, σ = 0.974, and n = 3
> 1. Among other things, the Container Store has grown and flourished because of strong customer relationships, which include listening to customer needs, providing products that meet customer needs, having salespeople who understand both customer needs an
> The successful Clarkson knife-gate valve contains a wafer that is thin and light. Yet, the wafer is so strong it can operate with up to 150 pounds-per-square-inch (psi) of pressure on it, making it much stronger than those of competing brands. Suppose Em
> 1. Suppose a fast-food analyst is interested in determining if there is a difference between Denver and Chicago in the average price of a comparable hamburger. There is some indication, based on information published by Burger Week, that the average pric
> 1. Many proportions were generated in the focus groups and market research that were conducted for this project, including the proportion of the market that is Hispanic, the proportion of Hispanic grocery shoppers that are women, the proportion of chip p
> Suppose you are using a completely randomized design to study some phenomenon. There are five treatment levels and a total of 55 people in the study. Each treatment level has the same sample size. Complete the following ANOVA.
> Compute a one-way ANOVA on the following data. 1 …………….….. 2 27 ………….… 22 31 ….……….… 27 31 …...…….… 25 29 ………….… 23 30 ………….… 26 27 ………….… 27 28 ………….… 23 Determine the observed F value. Compare it to the critical table F value and decide whether to rej
> Develop a one-way ANOVA on the following data. Determine the observed F value. Compare it to the critical F value and decide whether to reject the null hypothesis. Use a 1% level of significance.
> Discuss the following Minitab output. Analysis of Variance Means
> What proportion of commercial airline pilots are more than 40 years of age? Suppose a business analyst has access to a list of all pilots who are members of the Commercial Airline Pilots Association. If this list is used as a frame for the study, she can
> Study the following Minitab output. Determine whether there are any significant effects and discuss the results. What kind of design was used and what was the size of it? Analysis of Variance
> Interpret the following Excel output. Discuss the structure of the experimental design and any significant effects. Alpha is .05. ANOVA: Two-Factor Without Replication
> Study the following Minitab output and graph. Discuss the meaning of the output. Analysis of Variance for Dependent Variable
> Following is Excel output for an ANOVA problem. Describe the experimental design. The given value of alpha was .05. Discuss the output in terms of significant findings. ANOVA: Two-Factor Without Replication
> Analyze the following Minitab output. Describe the design of the experiment. Using α = .05, determine whether there are any significant effects; if so, explain why. Discuss any other ramifications of the output. Analysis of Variance
> Are some office jobs viewed as having more status than others? Suppose a study is conducted in which eight unemployed people are interviewed. The people are asked to rate each of five positions on a scale from 1 to 10 to indicate the status of the positi
> Why are mergers attractive to CEOs? One of the reasons might be a potential increase in market share that can come with the pooling of company markets. Suppose a random survey of CEOs is taken, and they are asked to respond on a scale from 1 to 5 (5 repr
> Compute a one-way ANOVA on the following data. Determine the observed F value. Compare the observed F value with the critical table F value and decide whether to reject the null hypothesis. Use α = .01.
> The Construction Labor Research Council lists a number of construction labor jobs that seem to pay approximately the same wages per hour. Some of these are bricklaying, iron working, and crane operation. Suppose a labor analyst takes a random sample of w
> Agricultural analysts are studying three different ways of planting peanuts to determine whether significantly different levels of production yield will result. The analysts have access to a large peanut farm on which to conduct their tests. They identif
> The highway department wants to estimate the proportion of vehicles on Interstate 25 between the hours of midnight and 5:00 a.m. that are 18-wheel tractor trailers. The estimate will be used to determine highway repair and construction considerations and
> A major automobile manufacturer wants to know whether there is any difference in the average mileage of four different brands of tires (A, B, C, and D), because the manufacturer is trying to select the best supplier in terms of tire durability. The manuf
> A company conducted a consumer research project to ascertain customer service ratings from its customers. The customers were asked to rate the company on a scale from 1 to 7 on various quality characteristics. One question was the promptness of company r
> Compute a two-way ANOVA on the following data (α = .01).
> A two-way ANOVA has been computed on a factorial design. Treatment 1 has five levels and treatment 2 has two levels. Each cell contains four measures. Complete the following ANOVA table. Use α = .05 to test to determine significance of the
> Analyze the following data, gathered from a randomized block design using α = .05. If there is a significant difference in the treatment effects, use Tukey’s HSD test to do multiple comparisons.
> Complete the following ANOVA table and determine whether there is any significant difference in treatment effects. Let α = .05.
> Examine the structure of the following experimental design. Determine which of the three designs presented in the chapter would be most likely to characterize this structure. Discuss the variables and the levels of variables. Determine the degrees of fre
> Compute a one-way ANOVA on the following data. Let α = .01. Use the Tukey-Kramer procedure to conduct multiple comparisons for the means.
> Compute a one-way ANOVA on the following data. Determine the observed F value. Compare the observed F value with the critical table F value and decide whether to reject the null hypothesis. Use α = .05.
> You are asked to analyze a completely randomized design that has six treatment levels and a total of 42 measurements. Complete the following table, which contains some information from the study.
> What proportion of pizza restaurants that are primarily for walk-in business have a salad bar? Suppose that, in an effort to determine this figure, a random sample of 1250 of these restaurants across the United States based on the Yellow Pages is called.
> Complete the following ANOVA table.
> Compute a one-way ANOVA on the following data. Use α = .05. If there is a significant difference in treatment levels, use Tukey’s HSD to compute multiple comparisons. Let α = .05 for the multiple comparisons.
> Finish the computations in the Minitab ANOVA table shown below and determine the critical table F values. Interpret the analysis. Discuss this problem, including the structure of the design, the sample sizes, and decisions about the hypotheses. Analysis
> Study the following ANOVA table produced by using Minitab. Describe the design (number of treatments, sample sizes, etc.). Are there any significant effects? Discuss the output. Analysis of Variance for DV
> A shoe retailer conducted a study to determine whether there is a difference in the number of pairs of shoes sold per day by stores according to the number of competitors within a 1-mile radius and the location of the store. The company researchers selec
> Children are generally believed to have considerable influence over their parents in the purchase of certain items, particularly food and beverage items. To study this notion further, a study is conducted in which parents are asked to report how many foo
> Suppose the following data have been gathered from a study with a two-way factorial design. Use α = .05 and a two-way ANOVA to analyze the data. State your conclusions.
> The data gathered from a two-way factorial design follow. Use the two-way ANOVA to analyze these data. Let α = .01.
> Is there a difference in the family demographics of people who stay at motels? Suppose a study is conducted in which three categories of motels are used: economy motels, modestly priced chain motels, and exclusive motels. One of the dependent variables s
> According to the Stern Marketing Group, 9 out of 10 professional women say that financial planning is more important today than it was five years ago. Where do these women go for help in financial planning? Forty-seven percent use a financial advisor (br
> Complete the following two-way ANOVA table. Determine the critical table F values and reach conclusions about the hypotheses for effects. Let α = .05.
> Complete the following two-way ANOVA table. Determine the critical table F values and reach conclusions about the hypotheses for effects. Let α = .05.
> Describe the following factorial design. How many independent and dependent variables are there? How many levels are there for each treatment? If the data were known, could interaction be determined from this design? Compute all degrees of freedom. Each
> Describe the following factorial design. How many independent and dependent variables are there? How many levels are there for each treatment? If the data were known, could interaction be determined from this design? Compute all degrees of freedom. Each
> The comptroller of a company is interested in determining whether the average length of long-distance calls by managers varies according to type of telephone. A randomized block design experiment is set up in which a long-distance call by each of five ma
> As part of a manufacturing process, a plastic container is supposed to be filled with 46 ounces of saltwater solution. The plant has three machines that fill the containers. Managers are concerned that the machines might not be filling the containers wit
> In recent years, the debate over the U.S. economy has been constant. The electorate seems somewhat divided as to whether the economy is in a recovery or not. Suppose a survey was undertaken to ascertain whether the perception of economic recovery differs
> Safety in motels and hotels is a growing concern among travelers. Suppose a survey was conducted by the National Motel and Hotel Association to determine U.S. travelers’ perception of safety in various motel chains. The association chos
> A randomized block design has a treatment variable with four levels and a blocking variable with seven blocks. Using this information and α = .01, complete the following table and reach a conclusion about the null hypothesis.
> A randomized block design has a treatment variable with six levels and a blocking variable with 10 blocks. Using this information and α = .05, complete the following table and reach a conclusion about the null hypothesis.
> According to Music and Copyright, 2017, Universal Music Group is the music leader in combined physical and digital recorded music trade revenue. Suppose a business analyst wants to determine what market share the company holds in the city of St. Louis by
> A large multinational banking company wants to determine whether there is a significant difference in the average dollar amounts purchased by users of different types of credit cards. Among the credit cards being studied are MasterCard, Visa, Discover, a
> The following data were gathered from a randomized block design. Use α = .01 to test for a significant difference in the treatment levels. Establish the hypotheses and reach a conclusion about the null hypothesis.
> Use ANOVA to analyze the data from the randomized block design given here. Let α = .05. State the null and alternative hypotheses and determine whether the null hypothesis is rejected.
> Problem 11.16 analyzed the number of weekly hours worked per person at five different plants. An F value of 3.10 was obtained with a probability of .0266. Because the probability is less than .05, the null hypothesis is rejected at α = .05.
> Do multiple comparisons on the data in Problem 11.14 using Tukey’s HSD test and α = .05. State which pairs of cities, if any, have significantly different mean costs.
> Using α = .05, compute critical values using the Tukey-Kramer procedure for the pairwise groups in Problem 11.13. Determine which pairs of groups are significantly different, if any.
> Use Tukey’s HSD test to compute multiple comparisons for the data in Problem 11.12. Let α = .01. State which regions, if any, are significantly different from other regions in mean starting salary figures.
> Use the Tukey-Kramer procedure to do multiple comparisons for Problem 11.11. Let α = .01. State which pairs of machines, if any, produce significantly different mean fills.
> Using Problem 11.8, compute Tukey’s HSD and determine whether there is a significant difference in means by using this methodology. Let α = .05.
> Using the results from Problem 11.7, compute a Tukey’s HSD to determine whether there are any significant differences between group means. Let α = .01.
> Suppose a random sample of 85 items has been taken from a population and 40 of the items contain the characteristic of interest. Use this information to calculate a 90% confidence interval to estimate the proportion of the population that has the charact
> Use the Tukey-Kramer procedure to determine whether there is a significant difference between the means of groups 2 and 5 in Problem 11.6. Let α = .01.
> Southwest Airlines is able to keep fares low, in part because of relatively low maintenance costs on its airplanes. One of the main reasons for the low maintenance costs is that Southwest flies only one type of aircraft, the Boeing 737. However, Southwes
> Using the results of Problem 11.5, compute a critical value by using the Tukey-Kramer procedure for groups 1 and 2. Use α = .05. Determine whether there is a significant difference between these two groups.
> A completely randomized design has been analyzed by using a one-way ANOVA. There are four treatment groups in the design, and each sample size is six. MSE is equal to 2.389. Using α = .05, compute Tukey’s HSD for this ANOVA.
> Suppose an ANOVA has been performed on a completely randomized design containing six treatment levels. The mean for group 3 is 15.85, and the sample size for group 3 is eight. The mean for group 6 is 17.21, and the sample size for group 6 is seven. MSE i
> Business is very good for a chemical company. In fact, it is so good that workers are averaging more than 40 hours per week at each of the chemical company’s five plants. However, management is not certain whether there is a difference
> Shown here is the Minitab output for a one-way ANOVA. Analyze the results. Include the number of treatment levels, the sample sizes, the F value, the overall statistical significance of the test, and the values of the means. Analysis of Variance Means
> Family transportation costs are usually higher than most people believe because those costs include car payments, insurance, fuel costs, repairs, parking, and public transportation. Twenty randomly selected families in four major cities are asked to use
> A management consulting company presents a three-day seminar on project management to various clients. The seminar is basically the same each time it is given. However, sometimes it is presented to high-level managers, sometimes to midlevel managers, and
> That the starting salaries of new accounting graduates would differ according to geographic regions of the United States seems logical. A random selection of accounting firms is taken from three geographic regions, and each is asked to state the starting
> Use the following sample information to calculate the confidence interval to estimate the population proportion. Let x be the number of items in the sample having the characteristic of interest. a) n = 116 and x = 57, with 99% confidence b) n = 800 and x
> A milk company has four machines that fill gallon jugs with milk. The quality-control manager is interested in determining whether the average fill for these machines is the same. The following data represent random samples of fill measures (in quarts) f
> Suppose you are using a completely randomized design to study some phenomenon. There are three treatment levels and a total of 17 people in the study. Complete the following ANOVA table. Use α = .05 to find the table F value and use the dat
> Some New York Stock Exchange analysts believe that 24-hour trading on the stock exchange is the wave of the future. As an initial test of this idea, the New York St Exchange opened two after-hour “crossing sections” in the early 1990s and studied the res
> Employee suggestions can provide useful and insightful ideas for management. Some companies solicit and receive employee suggestions more than others, and company culture influences the use of employee suggestions. Suppose a study is conducted to determi
> Suppose a market analyst wants to determine the difference in the average price of a gallon of whole milk in Seattle and Atlanta. To do so, he takes a telephone survey of 21 randomly selected consumers in Seattle who have purchased a gallon of milk and a
> A manufacturing company produces plastic pipes that are specified to be 10 inches long and 1/8 inch thick with an opening of 3/4 inch. These pipes are molded on two different machines. To maintain consistency, the company periodically randomly selects pi
> A large manufacturing company produces computer printers that are distributed and sold all over the United States. Due to lack of industry information, the company has a difficult time ascertaining its market share in different parts of the country. They
> Why do employees “blow the whistle” on other employees for unethical or illegal behavior? One study conducted by the AICPA reported the likelihood that employees would blow the whistle on another employee for such thin
> Information presented by GraphicSprings showed some of the highest and the lowest global rental rates per year per square foot of office space. Among the cities with the lowest rates were Houston, Riyadh, Melbourne, Amsterdam, and Bengaluru, with rental
> For the two large newspapers in your city, you are interested in knowing whether there is a significant difference in the average number of pages in each dedicated solely to advertising. You randomly select 10 editions of newspaper A and 6 editions of ne
> Use the information about each of the following samples to compute the confidence interval to estimate p. a) n = 44 and p^ = .51; compute a 90% confidence interval. b) n = 300 and p^ =.82; compute a 95% confidence interval. c) n = 1150 and p^ = .48; comp