Introduction to Probability and Statistics for Engineers and Scientists

Problems 287

having varianceσi^2 ,i=1, 2, compute a 95 percent two-sided confidence interval

forσ 12 /σ 22 when the data are as follows:

Coded Measures of Hardness

Analyst 1 Analyst 2

.46 .82

.62 .61

.37 .89

.40 .51

.44 .33

.58 .48

.48 .23

.53 .25

.67

.88

47.A problem of interest in baseball is whether a sacrifice bunt is a good strategy

when there is a man on first base and no outs. Assuming that the bunter will

be out but will be successful in advancing the man on base, we could compare

the probability of scoring a run with a player on first base and no outs with

the probability of scoring a run with a player on second base and one out. The

following data resulted from a study of randomly chosen major league baseball

games played in 1959 and 1960.

(a) Give a 95 percent confidence interval estimate for the probability of scoring

at least one run when there is a man on first and no outs.

(b) Give a 95 percent confidence interval estimate for the probability of scoring

at least one run when there is a man on second and one out.

Number of Cases

Number in Which 0 Runs Total Number

Base Occupied of Outs Are Scored of Cases

First 0 1,044 1,728

Second 1 401 657

48.A random sample of 1,200 engineers included 48 Hispanic Americans, 80 African

Americans, and 204 females. Determine 90 percent confidence intervals for the

proportion of all engineers that are

(a) female;

(b) Hispanic Americans or African Americans.