Austin King
5/12/15
DSCI 346-01
On-Paper Assignment Chapter 11

11.43
Budget shortfalls in many states during the most recent recession placed a strain on education resources. One area that receives much attention from both parents and administrators is the number of the students per teacher. Suppose the U.S. Department of Education would like to compare this ratio in kindergartens for schools in California, Delaware, Nevada, and Georgia. The following data show the number of kindergarten students in randomly selected classrooms in these four states. These data can also be found in the Excel file kindergarten.xlsx. a. Perform a one-way ANOVA using α= 0.05 to determine if the average number of students in kindergarten classes is different in the four states.

b. If warranted, perform a multiple comparison test to determine which pairs are different using α=0.05.

c. Verify your results with Minitab.
11.47
Suppose Scotts Lawn Care would like to test the effectiveness of four new grass fertilizers that it has developed. Each fertilizer is applied to identical-size sections of grass, and after a period of time the sections of grass are mowed. The weight of the grass clippings are used to measure the effectiveness of the fertilizer. To control for variations in soil and ambient conditions, each fertilizer was applied to five different lawns, which can act as a blocking factor. The pounds of grass clippings for each sample are shown in the following table. These data can also be found in the Excel file fertilizer.xlsx. a. Using a randomized block ANOVA and α=0.05, does there appear to be a difference in the effectiveness of the four fertilizers?

b. If the answer to part a is no, what additional steps should be taken to test the difference in the population means of each fertilizer?

c. If warranted, determine which pairs of fertilizers were different using α=0.05.

d. Verify your results with Minitab

11.55
Suppose the Department of Energy would like to compare residential utility bills for different cities in the United States. A random sample of households was selected, and their utility bills for the month were recorded. The number of bedrooms in the houses was also noted. These data can also be found in the file utility bills.xlsx. a. Using α= 0.05, is there significant interaction between the number of bedrooms and the city?

b. Using a two-way ANOVA and α=0.05, does the number of bedrooms have an effect on the average monthly utility bill?

c. Using a two-way ANOVA and α=0.05, does the city have an effect on the average monthly utility bill?

d. If warranted, determine which means are significantly different using α=0.05

e. Construct an interaction plot for the number of bedrooms and the city.