Exam 11: B: The Analysis of Variance

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.

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. Use the p-value approach to determine whether there is a significant difference in the prices charged by the three stores at the 0.05 level of significance.

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.

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. Use the p-value approach to determine whether there is a significant difference in the price of tools. What does this tell you about the appropriateness of the experimental design? Explain your reasoning.

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.

Randomized Block Design Narrative The partially completed ANOVA table for a randomized block design is presented below: -Refer to Randomized Block Design Narrative. Fill in the blanks in the ANOVA table.

Salary of Business Graduates Narrative An economist wants to test whether the mean starting salary (in $1000s) of business graduates is the same for three different majors and three types of class standing (top third, middle third, lowest third). No interaction is assumed. Appropriate sampling reveals the data shown below. Starting Salaries (thousands of dollars per year) -Refer to Salary of Business Graduates Narrative. Do the data present sufficient evidence to indicate differences among the block means? Why or why not? (Test using α = 0.05.)

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.

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.

Keyboard and Word Processing Narrative The data shown below were taken from a 2 * 3 factorial experiment to examine the effects of factor A (keyboard configuration, 3 levels) and factor B (word processing package, 2 levels). Each cell consists of four replicates, representing the number of minutes each of four secretaries randomly assigned to that cell required to type a standard document. Factor B -Refer to Keyboard and Word Processing Narrative. Is there sufficient evidence at the 5% significance level to infer that factors A and B interact? Explain why or why not.

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.

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.

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.

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.

3 * 3 Factorial Experiment Narrative The table below gives data for a 3 * 3 factorial experiment, with two replications per treatment: Levels of Factor A -Refer to 3 *3 Factorial Experiment Narrative. Find the approximate p-value for the test in the previous question. Use statistical software or Excel and report the exact p-value.

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 error degrees of freedom?

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. Based on your answer to the previous question, is testing for the main effects, plan and shift, appropriate? Give reasons for your answer.

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.

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?

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.