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
|
|
|
|
|
|
|
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a) Use a calculator with mean and standard deviation keys to verify that x-bar = ~2.29 and s = ~1.40.
b) Compute a 90% confidence interval for the population mean mu of home run percentages for all professional baseball players.
c) Compute a 99% confidence interval for the population mean mu of home run percentages for all professional baseball players.
d) The home run percentages for three professional players are: Tim Huelett 2.5, Herb Hunter 2.0, and Jackie Jensen 3.8.
Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.
Huelett and Hunter are in the 99% CI range; Jensen is above the range
e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not?