Deck 11: B: The Analysis of Variance

Question 1

Manufacturing Plant Machines
A mechanical engineer at a manufacturing plant keeps a close watch on the performance and condition of the machines. The following data are the weight losses (in milligrams) of certain machine parts due to friction when used with three different lubricants.
Refer to Manufacturing Plant Machines graphics. Set up the ANOVA Table.

Answer 1

Question 2

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. Calculate the value of the test statistic F.

Answer 2

= 102,985, = 1,357, = 463, = 411, and = 483. The correction for the mean is CM = = /18 = 102,302.722. Then, Total SS = = 102,985 - 102,302.722 = 682.278. SST = = 102,763.1667 - 102,302.722 = 460.445. MST = SST/(k - 1) = 460.445/2 = 230.223. SSE = Total SS - SST = 682.278 - 460.445 = 221.833. MSE = SSE/(n - k) = 221.833/15 = 14.789. The value of the test statistic is F = MST/MSE = 230.223/14.789 = 15.567.

Question 3

Breaking Strength of Thread Narrative
A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. = 6605.02, and = 362.2
Refer to Breaking Strength of Thread Narrative. Set up the rejection region for = 0.05.

Answer 3

With = 3, = 16, and = 0.10, the rejection region is reject if F > = 2.46.

Question 4

Breaking Strength of Thread Narrative
A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. = 6605.02, and = 362.2
Refer to Breaking Strength of Thread Narrative. State the null and alternative hypotheses to test whether there is a significant difference in mean breaking strength of the four kinds of thread.

Question 5

Breaking Strength of Thread Narrative
A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. = 6605.02, and = 362.2
Refer to Breaking Strength of Thread Narrative. Calculate the test statistic.

Question 6

Manufacturing Plant Machines
A mechanical engineer at a manufacturing plant keeps a close watch on the performance and condition of the machines. The following data are the weight losses (in milligrams) of certain machine parts due to friction when used with three different lubricants.
Refer to Manufacturing Plant Machines graphics. Calculate the value of the test statistic F.

Question 7

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. Develop and interpret a 95% confidence interval for .

Question 8

Manufacturing Plant Machines
A mechanical engineer at a manufacturing plant keeps a close watch on the performance and condition of the machines. The following data are the weight losses (in milligrams) of certain machine parts due to friction when used with three different lubricants.
Refer to Manufacturing Plant Machines graphics. Set up the rejection region for = 0.01.

Question 9

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. What is the appropriate conclusion for the test?

Question 10

Breaking Strength of Thread Narrative
A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. = 6605.02, and = 362.2

-Refer to Breaking Strength of Thread Narrative. What conclusion can be drawn? Give reasons for your answer.

Question 11

Manufacturing Plant Machines
A mechanical engineer at a manufacturing plant keeps a close watch on the performance and condition of the machines. The following data are the weight losses (in milligrams) of certain machine parts due to friction when used with three different lubricants.
Refer to Manufacturing Plant Machines graphics. How many degrees of freedom are associated with the F test statistic?

Question 12

Manufacturing Plant Machines
A mechanical engineer at a manufacturing plant keeps a close watch on the performance and condition of the machines. The following data are the weight losses (in milligrams) of certain machine parts due to friction when used with three different lubricants.

-Refer to Manufacturing Plant Machines graphics. What is the appropriate conclusion for the test?

Question 13

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. Develop a 95% confidence interval for .

Question 14

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. How many degrees of freedom are associated with the F test statistic?

Question 15

Breaking Strength of Thread Narrative
A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. = 6605.02, and = 362.2

-Refer to Breaking Strength of Thread Narrative. Find and interpret the approximate p-value.

Question 16

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. State the null and alternative hypotheses to test the hypothesis of equality of the mean whiteness readings for the three detergents.

Question 17

Manufacturing Plant Machines
A mechanical engineer at a manufacturing plant keeps a close watch on the performance and condition of the machines. The following data are the weight losses (in milligrams) of certain machine parts due to friction when used with three different lubricants.
Refer to Manufacturing Plant Machines graphics. State the null and alternative hypotheses to test whether there is a significant difference in mean weight losses among the three lubricants.

Question 18

Breaking Strength of Thread Narrative
A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. = 6605.02, and = 362.2
Refer to Breaking Strength of Thread Narrative. Set up the ANOVA Table

Question 19

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. Set up the rejection region for = 0.05.

Question 20

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
Refer to Laundry Detergent Preference Narrative. Set up the ANOVA Table.

Question 21

Due to his high blood pressure, Sam watches the sodium content of the foods that he eats. Five samples for each of four brands of canned turkey (97% fat free) were tested for sodium content, measured in milligrams of sodium per 60 gram serving. The following summary table and ANOVA were generated by statistical software as shown below: Use the p-value approach to test whether there is a significant difference in mean amount of sodium in the four brands. Let = 0.05.

Question 22

Lifetime of Brake Shoes Narrative
An automobile parts store was interested in comparing the mean life length of three brands of automobile brake shoes. The following data represent the life length, measured in 1000s of kilometres, of random samples of six sets of brake shoes of each brand:
Refer to Lifetime of Brake Shoes Narrative. State the null and alternative hypotheses to test whether there is a significant difference in mean life length among the three brands of brake shoes. Let = 0.05.

Question 23

Laptop Battery Charge Time Narrative
A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6
Refer to Laptop Battery Charge Time Narrative. What conclusion can be drawn? Provide a reason for your answer.

Question 24

Lifetime of Brake Shoes Narrative
An automobile parts store was interested in comparing the mean life length of three brands of automobile brake shoes. The following data represent the life length, measured in 1000s of kilometres, of random samples of six sets of brake shoes of each brand:

-Refer to Lifetime of Brake Shoes Narrative. Perform the test using the p-value approach.

Question 25

Laptop Battery Charge Time Narrative
A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6
Refer to Laptop Battery Charge Time Narrative. Set up the rejection region for = 0.01.

Question 26

Fill in the blanks (identified by asterisks) in the following partial ANOVA table:

Question 27

Laptop Battery Charge Time Narrative
A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6
Refer to Laptop Battery Charge Time Narrative. Set up the ANOVA Table.

Question 28

Breaking Strength of Thread Narrative
A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. = 6605.02, and = 362.2
Refer to Breaking Strength of Thread Narrative. Find and interpret a 90% confidence interval for .

Question 29

The following statistics were calculated based on samples drawn from three normal populations:
Treatment Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means.

Question 30

Ann Day wishes to determine if the mean price of grocery items is the same for five supermarkets in her city. The same seven food (and brand) items were priced at the five stores. Complete the partial ANOVA table below for testing the null hypothesis of no difference in the true mean price for the five stores in a completely randomized design. Can you reject the null hypothesis? Use = 0.05.

Question 31

Laptop Battery Charge Time Narrative
A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6
Refer to Laptop Battery Charge Time Narrative. Develop and interpret a 90% confidence interval for .

Question 32

A travel agency primarily reserves flights with four major airlines. The agency would like to know if the true mean price for the four airlines is the same. Below are the prices for flights leaving from the same city travelling to five different destinations. Test the null hypothesis of no difference in the true mean price for the four airlines in a completely randomized design. Use $\alpha$ = 0.05.

Question 33

Laptop Battery Charge Time Narrative
A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6
Refer to Laptop Battery Charge Time Narrative. Calculate the test statistic.

Question 34

Based on public demand, price for seeds, and average yield, a farmer must choose which variety of wheat to grow. In the first step toward making a decision, the farmer planted eight test plots each with three varieties of wheat. The recorded yields (in kilograms per plot) were used in an analysis of variance. Use the output below from the analysis of variance to test the null hypothesis of no difference among the mean yields of the three varieties of wheat. Use $\alpha$ = 0.005 to draw conclusions.

Question 35

Laptop Battery Charge Time Narrative
A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6
Refer to Laptop Battery Charge Time Narrative. State the null and alternative hypothesis to test whether there is a significant difference in mean functioning time before needing recharging among the three brands of battery packs.

Question 36

Healthy Dog Food Narrative
A premium dog food manufacturer claims that, since its food is so highly nutritious, you won't need to feed your dog as much as with other dog foods. The premium dog food was compared to three other brands with respect to how much a dog needed to eat, in kilograms per week, to maintain its current weight and for the dog to remain healthy. A random sample of 24 similar dogs was selected and divided into 4 groups (i.e., 6 dogs were randomly assigned to each dog food brand). The following partial analysis table was computed:
Analysis of Variance for Dog Food Brands
Refer to Healthy Dog Food Narrative. State the null and alternative hypotheses to test whether there is a significant difference in the average amount of dog food needed to maintain a dog's current weight and for the dog to remain healthy.

Question 37

Healthy Dog Food Narrative
A premium dog food manufacturer claims that, since its food is so highly nutritious, you won't need to feed your dog as much as with other dog foods. The premium dog food was compared to three other brands with respect to how much a dog needed to eat, in kilograms per week, to maintain its current weight and for the dog to remain healthy. A random sample of 24 similar dogs was selected and divided into 4 groups (i.e., 6 dogs were randomly assigned to each dog food brand). The following partial analysis table was computed:
Analysis of Variance for Dog Food Brands
Refer to Healthy Dog Food Narrative. Complete the ANOVA table.

Question 38

Suppose a reading comprehension test is given to random samples of three Grade 7 students from each of five different schools. The samples are chosen so that each school provides a student categorized as low IQ, average IQ, and high IQ. Perform an analysis using the data below, treating the IQs as blocks. Is there sufficient evidence to reject the null hypothesis of no difference between the true mean test scores of the five schools? Draw conclusions using = 0.05.

Question 39

Laptop Battery Charge Time Narrative
A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6

-Refer to Laptop Battery Charge Time Narrative. Find and interpret the approximate p-value.

Question 40

Lifetime of Brake Shoes Narrative
An automobile parts store was interested in comparing the mean life length of three brands of automobile brake shoes. The following data represent the life length, measured in 1000s of kilometres, of random samples of six sets of brake shoes of each brand:
Refer to Lifetime of Brake Shoes Narrative. Use statistical software to produce the ANOVA Table.

Question 41

Healthy Dog Food Narrative
A premium dog food manufacturer claims that, since its food is so highly nutritious, you won't need to feed your dog as much as with other dog foods. The premium dog food was compared to three other brands with respect to how much a dog needed to eat, in kilograms per week, to maintain its current weight and for the dog to remain healthy. A random sample of 24 similar dogs was selected and divided into 4 groups (i.e., 6 dogs were randomly assigned to each dog food brand). The following partial analysis table was computed:
Analysis of Variance for Dog Food Brands
Refer to Healthy Dog Food Narrative. What is the value of the test statistic?

Question 42

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Calculate SSE and MSE.

Question 43

Water Samples Narrative
Water samples were taken at four different locations in a river to determine whether the quantity of dissolved oxygen, a measure of water pollution, varied from one location to another. Locations 1 and 2 were selected above an industrial plant, one near the shore and the other in midstream; location 3 was adjacent to the industrial water discharge for the plant; and location 4 was slightly downriver in midstream. Five water specimens were randomly selected at each location, but one specimen, corresponding to location 4, was lost in the laboratory. The data and an ANOVA computer printout are provided here (the greater the pollution, the lower the dissolved oxygen readings).
Refer to Water Samples Narrative. Do the data provide sufficient evidence to indicate a difference in the mean dissolved oxygen contents for the four locations? Justify your conclusion.

Question 44

Insurance Company Narrative
An insurance company is considering opening a new branch in Lethbridge. The company will choose the final location from two locations within the city. One of the factors in the decision is the annual family income (in thousands of dollars) of five families randomly sampled from a radius of five miles from the potential locations.
Refer to Insurance Company Narrative. Perform an F-test for one-way ANOVA at the 5% level of significance to determine whether the population means differ.

Question 45

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Find a 90% confidence interval for the difference ( ).

Question 46

Healthy Dog Food Narrative
A premium dog food manufacturer claims that, since its food is so highly nutritious, you won't need to feed your dog as much as with other dog foods. The premium dog food was compared to three other brands with respect to how much a dog needed to eat, in kilograms per week, to maintain its current weight and for the dog to remain healthy. A random sample of 24 similar dogs was selected and divided into 4 groups (i.e., 6 dogs were randomly assigned to each dog food brand). The following partial analysis table was computed:
Analysis of Variance for Dog Food Brands
Refer to Healthy Dog Food Narrative. Set up the rejection region using = 0.05.

Question 47

Healthy Dog Food Narrative
A premium dog food manufacturer claims that, since its food is so highly nutritious, you won't need to feed your dog as much as with other dog foods. The premium dog food was compared to three other brands with respect to how much a dog needed to eat, in kilograms per week, to maintain its current weight and for the dog to remain healthy. A random sample of 24 similar dogs was selected and divided into 4 groups (i.e., 6 dogs were randomly assigned to each dog food brand). The following partial analysis table was computed:
Analysis of Variance for Dog Food Brands

-Refer to Healthy Dog Food Narrative. What conclusion can be drawn? Explain.

Question 48

Water Samples Narrative
Water samples were taken at four different locations in a river to determine whether the quantity of dissolved oxygen, a measure of water pollution, varied from one location to another. Locations 1 and 2 were selected above an industrial plant, one near the shore and the other in midstream; location 3 was adjacent to the industrial water discharge for the plant; and location 4 was slightly downriver in midstream. Five water specimens were randomly selected at each location, but one specimen, corresponding to location 4, was lost in the laboratory. The data and an ANOVA computer printout are provided here (the greater the pollution, the lower the dissolved oxygen readings).
Refer to Water Samples Narrative. Compare the mean dissolved oxygen content in midstream above the plant with the mean content adjacent to the plant (location 2 versus location 3). Use a 95% confidence interval.

Question 49

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. State the null and alternative hypotheses for an analysis of variance F test.

Question 50

In a completely randomized design, 7 experimental units were assigned to the first treatment, 13 units to the second treatment, and 10 units to the third treatment. A partial ANOVA table for this experiment is shown below:
a. Fill in the blanks (identified by asterisks) in the above ANOVA Table.
b. Test at the 5% significance level to determine if differences exist among the three treatment means.

Question 51

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Do the data provide sufficient evidence to indicate a difference between and ? Justify your conclusion. Test using the two-sample independent t test with = 0.05.

Question 52

Physicians depend on laboratory test results when managing medical s such as diabetes or epilepsy. In a uniformity test for glucose tolerance, three different laboratories each sent = 5 identical blood samples from a person who had drunk 50 milligrams (mg) of glucose dissolved in water. The laboratory results (in mg/dL) are listed here: Do the data indicate a difference in the average readings for the three laboratories? Give reasons for your answer.

Question 53

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Calculate SST and MST.

Question 54

Insurance Company Narrative
An insurance company is considering opening a new branch in Lethbridge. The company will choose the final location from two locations within the city. One of the factors in the decision is the annual family income (in thousands of dollars) of five families randomly sampled from a radius of five miles from the potential locations.
Refer to Insurance Company Narrative. If we want to determine whether the population mean income for area 2 is higher than that for area 1, can we still use both the t and F tests applied in the previous questions? Explain.

Question 55

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Construct an ANOVA table for the data.

Question 56

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Calculate CM and Total SS.

Question 57

Insurance Company Narrative
An insurance company is considering opening a new branch in Lethbridge. The company will choose the final location from two locations within the city. One of the factors in the decision is the annual family income (in thousands of dollars) of five families randomly sampled from a radius of five miles from the potential locations.
Refer to Insurance Company Narrative. What is the mathematical relationship between the observed t and observed F-test statistics from the previous two questions? Does the same relation hold true for the corresponding critical values? Why or why not?

Question 58

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Use the p-value approach to determine whether there is a difference in the three population means.

Question 59

Absenteeism Narrative
The data shown below are collected using randomized design. The data values represent the number of days absent from work for three independent samples of workers.
Refer to Absenteeism Narrative. Find a 90% confidence interval for .

Question 60

Insurance Company Narrative
An insurance company is considering opening a new branch in Lethbridge. The company will choose the final location from two locations within the city. One of the factors in the decision is the annual family income (in thousands of dollars) of five families randomly sampled from a radius of five miles from the potential locations.
Refer to Insurance Company Narrative. Perform an equal-variances t test at the 5% significance level to determine whether the population means differ.

Question 61

A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information: = 1150.72, and = 165.6
Use Tukey's method of comparison to determine which of the three battery pack means differ from the others. Let = 0.05.

Question 62

Due to his high blood pressure, Sam watches the sodium content of the foods that he eats. Five samples for each of four brands of canned turkey (97% fat free) were tested for sodium content, measured in milligrams of sodium per 60 gram serving. The following summary table and ANOVA were generated by statistical software as shown below: Use the following output generated by statistical software to determine which of the means are different.
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0113
Critical value = 4.05
Intervals for (column level mean) - (row level mean)

Question 63

Travel Agency Narrative
A travel agency primarily reserves flights with four major airlines. The agency would like to know if the true mean price for the four airlines is the same. Below are the prices for flights leaving from the same city and travelling to five different destinations.

-Refer to Travel Agency Narrative. Perform an analysis of variance treating the destinations as blocks. Use $\alpha$ = 0.05.

Question 64

Supermarket Prices Narrative
A building contractor employs three construction engineers, A, B, and C to estimate and bid on jobs. To determine whether one tends to be a more conservative (or liberal) estimator than the others, the contractor selects four projected construction jobs and has each estimator independently estimate the cost (in dollars per square foot) of each job. The data are shown in the table:
Construction Job
Refer to Supermarket Prices Narrative. Analyze the experiment using the appropriate methods. Identify the blocks and treatments, and investigate any possible differences in treatment means.

Question 65

Treatment Observation Narrative
An independent random sampling design was used to compare the means of six treatments based on samples of four observations per treatment. The pooled estimator of is 9.42, and the sample means follow: = 102.1, = 98.9, = 112.8, = 93.4, = 104.7, and = 114.3.
Refer to Treatment Observation Narrative. Give the value of that you would use to make pairwise comparisons of the treatment means for = 0.05.

Question 66

A study was conducted to compare fuel consumption of medium-size trucks for three brands of gasoline, A, B, and C. Four trucks of the same make and model were used in the experiment, and each gasoline brand was tested in each truck. Using each brand in the same truck has the effect of eliminating (blocking out) truck-to-truck variability. The data (litres per 100 km) are as follows:
Automobile Use an appropriate method to identify the pairwise differences, if any, in the average fuel consumptions for the three brands of gasoline.

Question 67

In order to examine the differences in ages of teachers among five school districts, an educational statistician took random samples of six teachers' ages in each district. The data are listed below.
Ages of Teachers among Five School Districts Use Tukey's multiple comparison method to determine which means differ.

Question 68

Supermarket Prices Narrative
A building contractor employs three construction engineers, A, B, and C to estimate and bid on jobs. To determine whether one tends to be a more conservative (or liberal) estimator than the others, the contractor selects four projected construction jobs and has each estimator independently estimate the cost (in dollars per square foot) of each job. The data are shown in the table:
Construction Job
Refer to Supermarket Prices Narrative. If any differences in treatment means exist, use an appropriate method to identify specifically where the differences lie. Has blocking been effective in this experiment? Explain.

Question 69

Travel Agency Narrative
A travel agency primarily reserves flights with four major airlines. The agency would like to know if the true mean price for the four airlines is the same. Below are the prices for flights leaving from the same city and travelling to five different destinations.
Refer to Travel Agency Narrative. Why is it necessary to treat the destinations as blocks? Justify your answer.

Question 70

Travel Agency Narrative
A travel agency primarily reserves flights with four major airlines. The agency would like to know if the true mean price for the four airlines is the same. Below are the prices for flights leaving from the same city and travelling to five different destinations.
Refer to Travel Agency Narrative. Develop and interpret a 90% confidence interval for .

Question 71

The data that follow are observations collected from an experiment that compared four treatments, A, B, C, and D, within each of three blocks, using a randomized block design.
Treatment Rank the four treatment means using Tukey's method of paired comparisons with = 0.01.

Question 72

Tool Prices Comparison Narrative
A consumer was interested in determining whether there is a significant difference in the price charged for tools by three hardware stores. The consumer selected five tools and recorded the price for each tool in each store. The following data was recorded:
Tools
Refer to Tool Prices Comparison Narrative. What is the appropriate experimental design?

Question 73

Travel Agency Narrative
A travel agency primarily reserves flights with four major airlines. The agency would like to know if the true mean price for the four airlines is the same. Below are the prices for flights leaving from the same city and travelling to five different destinations.
Refer to Travel Agency Narrative. Develop and interpret a 90% confidence interval for .

Question 74

Physicians depend on laboratory test results when managing medical s such as diabetes or epilepsy. In a uniformity test for glucose tolerance, three different laboratories each sent = 5 identical blood samples from a person who had drunk 50 milligrams (mg) of glucose dissolved in water. The laboratory results (in mg/dL) are listed here: Use Tukey's method for paired comparisons to rank the three treatment means. Use = 0.05.

Question 75

Supermarket Prices Narrative
A building contractor employs three construction engineers, A, B, and C to estimate and bid on jobs. To determine whether one tends to be a more conservative (or liberal) estimator than the others, the contractor selects four projected construction jobs and has each estimator independently estimate the cost (in dollars per square foot) of each job. The data are shown in the table:
Construction Job

-Refer to Supermarket Prices Narrative. Complete the ANOVA table below where the grocery items were treated as blocks. Can you reject the null hypothesis of no difference between the true mean price for the five stores? Use $\alpha$ = 0.05.

Question 76

An automobile parts store was interested in comparing the mean life length of three brands of automobile brake shoes. The following data represent the life length, measured in thousands of kilometres, of random samples of six sets of brake shoes of each brand: Use the following output from statistical software to determine which of the means differ at the 0.05 level of significance.
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0203
Critical value = 3.67
Intervals for (column level mean) - (row level mean)

Question 77

Wrapping Colour Narrative
A firm's product can be wrapped in any of three colours: red, white, and black. The manager wants to test whether mean monthly sales (in $1000s) are the same, regardless of the colour. Viewing the past five months as a random sample, the manager collected the data shown below.
Sales History (thousands of dollars)
Refer to Wrapping Colour Narrative. State the appropriate null and alternative hypotheses.

Question 78

Supermarket Prices Narrative
A building contractor employs three construction engineers, A, B, and C to estimate and bid on jobs. To determine whether one tends to be a more conservative (or liberal) estimator than the others, the contractor selects four projected construction jobs and has each estimator independently estimate the cost (in dollars per square foot) of each job. The data are shown in the table:
Construction Job
Refer to Supermarket Prices Narrative. Why is it important to treat the food items as blocks? (Hint: The observed value of the test statistic in a completely randomized design is F = 0.089, and = 2.69).

Question 79

Wrapping Colour Narrative
A firm's product can be wrapped in any of three colours: red, white, and black. The manager wants to test whether mean monthly sales (in $1000s) are the same, regardless of the colour. Viewing the past five months as a random sample, the manager collected the data shown below.
Sales History (thousands of dollars)
Refer to Wrapping Colour Narrative. Perform the test at the 1% level of significance.

Question 80

Wrapping Colour Narrative
A firm's product can be wrapped in any of three colours: red, white, and black. The manager wants to test whether mean monthly sales (in $1000s) are the same, regardless of the colour. Viewing the past five months as a random sample, the manager collected the data shown below.
Sales History (thousands of dollars)
Refer to Wrapping Colour Narrative. Create the appropriate ANOVA table.