Chapter 13.10, Problem 55E

Refer to Exercise 13.46. Construct a 95% confidence interval for the difference in the mean distance of roll when Dasher ryegrass and Marvelgreen supreme are used for overseeding.

13.46 A. E. Dudeck and C. H. Peacock report on an experiment conducted to evaluate the performance of several cool-season grasses for winter overseeding of golf greens in northern Florida. One of the variables of interest was the distance that a golf ball would roll on a green after being rolled down a ramp (used to induce a constant initial velocity to the ball). Because the distance that the ball would roll was influenced by the slope of the green and the direction in which the grass was mowed, the experiment was set up in a randomized block design. The blocks were determined so that the slopes of the individual plots were constant within blocks (a transit was used to ensure accuracy), and all plots were mowed in the same direction and at the same height to eliminate mowing effects. The base grass was “Tiftgreen” Bermuda grass in a semidormant state. The same method of seeding and rates of application were used for all the ryegrasses that are represented in the following table of data. Measurements are average distances (in meters) from the base of the ramp to the stopping points for five balls rolled down the ramp and directly up the slope on each plot. Cultivars used in the study included A (Pennfine ryegrass), B (Dasher ryegrass), C (Regal ryegrass), D (Marvelgreen supreme), and E (Barry ryegrass). The grasses were planted within blocks and yielded the measurements shown.⁷

a Perform the appropriate ANOVA to test for sufficient evidence to indicate that the mean distance of ball roll differs for the five cultivars. Give bounds for the attained significance level. What would you conclude at the α = .01 level of significance?

b Is there evidence of a significant difference between the blocks used in the experiment? Test using α = .05.