Exam 11: B: The Analysis of Variance

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?

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 .

Running Shoes Narrative An avid runner was interested in whether there is a significant difference in the average wear (measured in weeks of use) among three brands of running shoes. To answer the question, the runner randomly selected six runners and assigned them to wear each of the three brands of running shoes until the shoes wore out. Each of the runners wore the brands of shoes in a random order. After the data had been recorded, the following output was generated using statistical software: Two-way Analysis of Variance -Refer to Running Shoes Narrative. Is blocking necessary in this ? Justify your answer. Let = 0.05.

Randomized Block Design Narrative The partially completed ANOVA table for a randomized block design is presented below: -Refer to Randomized Block Design Narrative. How many observations are in each block total?

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.

UBC Building Signs Narrative A researcher at University of British Columbia (UBC) wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. A partial computer output of the appropriate analysis is given below: ANOVA Table -Refer to UBC Building Signs Narrative. What are the degrees of freedom for the interaction between the levels of signs and starting location?

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 .

Automobile Repair Cost Narrative Automobile insurance appraisers examine cars that have been involved in accidental collisions and estimate the cost of repairs. An insurance executive claims that there are significant differences in the estimates from different appraisers. To support his claim, he takes a random sample of six cars that have recently been damaged in accidents. Three appraisers then estimate the repair costs of all six cars. The data are shown below. Estimated Repair Cost -Refer to Automobile Repair Cost Narrative. Set up the ANOVA Table. Use α = 0.05 to determine the critical values.

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.

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.

Randomized Block Design Narrative The partially completed ANOVA table for a randomized block design is presented below: -Refer to Randomized Block Design Narrative. Do the data present sufficient evidence to indicate differences among the block means? Why or why not? (Test using = 0.05.)

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.

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 .

Automobile Repair Cost Narrative Automobile insurance appraisers examine cars that have been involved in accidental collisions and estimate the cost of repairs. An insurance executive claims that there are significant differences in the estimates from different appraisers. To support his claim, he takes a random sample of six cars that have recently been damaged in accidents. Three appraisers then estimate the repair costs of all six cars. The data are shown below. Estimated Repair Cost -Refer to Automobile Repair Cost Narrative. Can we infer at the 5% significance level that the executive's claim is true? Provide a justification for your conclusion.

Incentive Pay Narrative A company conducted an experiment to determine the effect of two types of incentive pay plans on worker productivity for workers of two shifts. The company used an equal number of production workers from each of the two shifts and one-half of these workers were assigned to each plan. Then five workers from each pay plan-shift combination were selected and their productivity (in number of items produced) recorded for a one-week period. The following output was generated using statistical software: Two-way analysis of variance -Refer to Incentive Pay Narrative. Is there significant interaction present in this ? Justify your answer. (Let = 0.05.)

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.

Product Markup Narrative A chain of jewellery stores conducted an experiment to investigate the relationship between price and location and the demand for its diamonds. Six small-town stores were selected for the study, as well as six stores located in large suburban malls. Two stores in each of these locations were assigned to each of three item percentage markups. The percentage gain (or loss) in sales for each store was recorded at the end of one month. The data are shown in the accompanying table. Markup -Refer to Product Markup Narrative. What are the practical implications of your test in the previous question?

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

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?

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.