Exam 13: Analysis of Variance Anova

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (colour neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Analysis of Kevin's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the critical F value is ___.

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Analysis of Kevin's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the appropriate decision is ___.

The statistical methods of analysis of variance assume that the populations are normally distributed.

For the following ANOVA table, the MS Treatment value is ___.

Pate's Pharmacy, Inc. operates a regional chain of 120 pharmacies. Each pharmacy's floor plan includes a greeting card department which is relatively isolated. Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department. She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level. Analysis of Sandra's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the critical F value is ___.

Data on three treatment levels are shown in the following table: For a one-way ANOVA, the Total Sum of Squares (SST) is ___.

For the following ANOVA table, the MS Error value is ___.

As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Analysis of the data yielded the following ANOVA table: Using $\alpha$ = 0.05, the critical F value is ___.

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table: Using $\alpha$ = 0.01, the appropriate decision is ___.

A completely randomized design has been analyzed by using a one-way ANOVA. There are three treatment groups in the design, and each sample size is four. The mean for group 1 is 25.00 and for group 3 it is 27.50. MSE is 3.19. Using α=0.05 there is a significant difference between these two groups.

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table: Using $\alpha$ = 0.01, the critical F value is ___.

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (colour neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Analysis of Kevin's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the observed F value is ___.

Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy, claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the appropriate decision is ___.

Data on three treatment levels are shown in the following table: For a one-way ANOVA using  = 0.05, the critical F value is ___.

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table: Using $\alpha$ = 0.01, the observed F value is ___.

Data on three treatment levels are shown in the following table: For a one-way ANOVA, the Between Sum of Squares (SSB) is ___.

The statistical methods of analysis of variance assume equal sample means.

Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy, claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Kathleen's null hypothesis is ___.

Analysis of variance may be used to test the differences in the means of more than two independent populations.

A large company buys thousands of lightbulbs every year. The company is currently considering four brands of lightbulbs to choose from and wants to investigate if the mean lifetimes of the 4 types of bulbs are the same. The research department randomly selected 7 bulbs of each type and test how long they lasted until they burned out. The research department then analyzed the data and obtained the following ANOVA table: a) Fill in the blanks of the partially completed ANOVA table. b) At test whether there are differences in the mean lifetimes of the four brands of lightbulbs.