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

(a) From the given data

= 2.29

s = 1.40

_____________

(b) 90% CI

t critical for df = n - 1 = 42 for = 0.1 is 1.68

The Lower Limit = - tcritical * s / sqrt(n) = 2.29 - 1.68 * 1.4 / sqrt(43) = 1.93

The Upper Limit = + tcritical * s / sqrt(n) = 2.29 + 1.68 * 1.4 / sqrt(43) = 2.65

The 90% CI is (1.93, 2.65)

____________

(b) 99% CI

t critical for df = n - 1 = 42 for = 0.01 is 2.698

The Lower Limit = - tcritical * s / sqrt(n) = 2.29 - 2.698 * 1.4 / sqrt(43) = 1.71

The Upper Limit = + tcritical * s / sqrt(n) = 2.29 + 2.698 * 1.4 / sqrt(43) = 2.87

The 99% CI is (1.71, 2.87)

____________

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