Question

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, 2.0, 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, 0.0, 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 %

Answer 1

Solution :

The sample mean is given as follows :

We have, n = 43

The standard deviation is given as follows :

b) The 90% confidence interval for the population mean μ is given as follows :

Where, t_{(0.10/2, n - 1)} is critical t value to construct 90% confidence interval.

We have,  

Using t-table we get, t_{(0.10/2, 43 - 1)} = 1.682

Hence, the 90% confidence interval for the population mean μ of home run percentages for all professional baseball players is,

Lower limit : 2.02%

Upper limit : 3.12%

c) The 99% confidence interval for the population mean μ is given as follows :

Where, t_{(0.01/2, n - 1)} is critical t value to construct 99% confidence interval.

We have,  

Using t-table we get, t_{(0.01/2, 43 - 1)} = 2.698

Hence, the 99% confidence interval for the population mean μ of home run percentages for all professional baseball players is,

Lower limit : 1.69%

Upper limit : 3.45%