Exam 11: B: The Analysis of Variance

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. In order to determine the critical value of the F ratio against which to test for differences between the levels of factor A, which numerator and which denominator, respectively, for df should we use?

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. What do we mean when we say that factors A and B interact? Do the data provide sufficient evidence to indicate interaction between factors A and B? Justify your answer. (Test at = 0.05.)

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. Do the data provide sufficient evidence to indicate that factors A and B affect the response variable? Explain why or why not. (Test at = 0.05.)

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.

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 different starting location?

Headache Treatments Narrative The following data were generated from a 2 * 2 factorial experiment with three replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs that physicians recommend to increase the effectiveness of the injections. Three headache patients were randomly selected for each combination of injection and drug. Factor B -Refer to Headache Treatments Narrative. Test at the 5% significance level to determine if differences exist among the levels of factor B.

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 blocks are involved in the design?

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 is the F test statistic for testing the interaction effect between the types of signs and the starting location?

Statistical Software Narrative A professor of statistics is trying to determine which of three statistical software programs is best for his students. He believes that the time (in hours) it takes a student to master particular software may be influenced by gender. A 3 * 2 factorial experiment with three replicates was designed, as shown below: Gender -Refer to Statistical Software Narrative. Is there sufficient evidence at the 10% significance level to infer that the time it takes a student to master software and the gender of the student interact? Justify your conclusion.

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 .

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.

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.

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. Perform an analysis of variance for the data, and present the results in an analysis of variance table.

Baseball Controversy Narrative In recent years a controversy has arisen in major league baseball. Some players have been accused of "doctoring" their bats to increase the distance the ball travels. However, a physics professor claims that the effect of doctoring is negligible. A major league manager decides to test the professor's claim. He doctors two bats by inserting cork into one and rubber into another. He then tells five players on his team to hit a ball with an undoctored bat and with the doctored bats. The distances are measured and listed below. Distance Ball Travels (in feet) -Refer to Baseball Controversy Narrative. Set up the ANOVA Table. Use = 0.05 to determine the critical values.

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. Test at the 5% significance level to determine if differences exist among the levels of factor A.

Fuel Consumption Study Narrative 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 follow: Automobile -Refer to Fuel Consumption Study Narrative. Is there evidence of a difference in mean fuel consumption for the four automobiles? Justify your conclusion.

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.

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.

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 statistical software to develop the ANOVA table.

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.