Question

The home run percentage is the number of home runs per 100 times at bat. A...

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

 1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

 x = % s = %

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

 lower limit % upper limit %

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

 lower limit % upper limit %

The statistical software output for this problem is :

One sample T confidence interval:
μ : Mean of variable

90% confidence interval results:

Variable Sample Mean Std. Err. DF L. Limit U. Limit
Data 2.2930233 0.2136638 42 1.9336509 2.6523956

99% confidence interval results:

Variable Sample Mean Std. Err. DF L. Limit U. Limit
Data 2.2930233 0.2136638 42 1.7165442 2.8695023

(a)

x = 2.29

s = 1.40

(b)

Lower limit = 1.93

Upper limit = 2.65

(c)

Lower limit = 1.72

Upper limit = 2.87