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

a. For the given data sample mean is

To find standard deviation

Create the following table.

data	data-mean	(data - mean)2
1.6	-0.693	0.480249
2.4	0.107	0.011449
1.2	-1.093	1.194649
6.6	4.307	18.550249
2.3	0.007	4.9E-5
0	-2.293	5.257849
1.8	-0.493	0.243049
2.5	0.207	0.042849
6.5	4.207	17.698849
1.8	-0.493	0.243049
2.7	0.407	0.165649
2	-0.293	0.085849
1.9	-0.393	0.154449
1.3	-0.993	0.986049
2.7	0.407	0.165649
1.7	-0.593	0.351649
1.3	-0.993	0.986049
2.1	-0.193	0.037249
2.8	0.507	0.257049
1.4	-0.893	0.797449
3.8	1.507	2.271049
2.1	-0.193	0.037249
3.4	1.107	1.225449
1.3	-0.993	0.986049
1.5	-0.793	0.628849
2.9	0.607	0.368449
2.6	0.307	0.094249
0	-2.293	5.257849
4.1	1.807	3.265249
2.9	0.607	0.368449
1.9	-0.393	0.154449
2.4	0.107	0.011449
0	-2.293	5.257849
1.8	-0.493	0.243049
3.1	0.807	0.651249
3.8	1.507	2.271049
3.2	0.907	0.822649
1.6	-0.693	0.480249
4.2	1.907	3.636649
0	-2.293	5.257849
1.2	-1.093	1.194649
1.8	-0.493	0.243049
2.4	0.107	0.011449

Find the sum of numbers in the last column to get.

So

b. As sample size is greater than 30, we can use z distribution to find CI

for 90% CI z value is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of Error is

Hence CI is

Lower limit is 1.94

Upper limit is 2.64

c. For 99% CI z value is 2.58 as P(-2.58<z<2.58)=0.99

So Margin of Error is

Hence CI is

Lower limit is 1.74

Upper limit is 2.84