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 ? of home run percentages for all professional baseball players. Hint: If you use the Student's tdistribution 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 ? of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

 lower limit % upper limit %

(A) Mean= (sum of all data values)/(number of data values)

setting the values, we get

mean = (1.6+2.4+...+1.8+2.4)/43 =98.6/43 = 2.29

Standard deviation =

setting the values, we get

standard deviation =

it gives, standard deviation = 1.40

(B) t critical value corresponding to 90% confidence level and degree of freedom = n-1 = 43-1 = 42

we get, t critical = 1.68

confidence interval formula is

CI =

where

setting the values in the above formula, we get

CI =

so, lower limit is 1.93 and upper limit is 2.65

(C) t critical value corresponding to 99% confidence level and degree of freedom = n-1 = 43-1 = 42

we get, t critical = 2.70

confidence interval formula is

CI =

where

setting the values in the above formula, we get

CI =

so, lower limit is 1.71 and upper limit is 2.87

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