Does the plot indicate any violation of the conditions underlying the use of the Is there sufficient evidence that the standard deviation in rebound coefficient for the

c. d.

e. 7.12 Find the value of F that locates an area in the lower tail of the F distribution; that is, find for the following specifications:

a. b.

c. d.

e.

7.13 Find approximate values for for the following specifications:

a. b.

c. d.

e.

7.14 Random samples of n

1 ⫽ 15 and n 2 ⫽ 10 were selected from populations 1 and 2, respec- tively. The corresponding sample standard deviations were s 1 ⫽ 5.3 and s 2 ⫽ 8.8.

a. Do the data provide sufficient evidence to indicate a difference in

and ?

b. Place a 95 confidence interval on the ratio of the variances .

c. What assumptions have you made concerning the data and populations when making

your calculations in parts a and b? Engin. 7.15 A soft-drink firm is evaluating an investment in a new type of canning machine. The com- pany has already determined that it will be able to fill more cans per day for the same cost if the new machines are installed. However, it must determine the variability of fills using the new machines, and wants the variability from the new machines to be equal to or smaller than that currently obtained using the old machines. A study is designed in which random samples of 61 cans are selected from the output of both types of machines and the amount of fill in ounces is determined. The data are summarized in the following table and boxplots. Summary Data for Canning Experiment Machine Type Sample Size Mean Standard Deviation Old 61 12.284 .231 New 61 12.197 .162 s 2 1 兾s 2 2 s 2 s 1 a ⫽ .05 a ⫽ .005, df 1 ⫽ 90, df 2 ⫽ 75 a ⫽ .001, df 1 ⫽ 35, df 2 ⫽ 35 a ⫽ .01, df 1 ⫽ 50, df 2 ⫽ 12 a ⫽ .025, df 1 ⫽ 35, df 2 ⫽ 15 a ⫽ .05, df 1 ⫽ 14, df 2 ⫽ 19 F a a ⫽ .005, df 1 ⫽ 8, df 2 ⫽ 13 a ⫽ .001, df 1 ⫽ 15, df 2 ⫽ 5 a ⫽ .01, df 1 ⫽ 10, df 2 ⫽ 12 a ⫽ .025, df 1 ⫽ 15, df 2 ⫽ 15 a ⫽ .05, df 1 ⫽ 5, df 2 ⫽ 15 F 1⫺ a a a ⫽ .005, df 1 ⫽ 8, df 2 ⫽ 13 a ⫽ .001, df 1 ⫽ 15, df 2 ⫽ 5 a ⫽ .01, df 1 ⫽ 10, df 2 ⫽ 12 12.8 12.3 11.8 Old machine New machine Boxplots of old machine and new machine means are indicated by solid circles