The home run percentage is the number of home runs per 100 timesat bat. A random sample of 43 professional baseball players gavethe 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 tofind x and s. (Round your answers to two decimalplaces.)
(b) Compute a 90% confidence interval for the population mean? of home run percentages for all professional baseballplayers. Hint: If you use the Student's tdistribution table, be sure to use the closest d.f. thatis smaller. (Round your answers to two decimalplaces.)
| lower limit | % |
| upper limit | % |
(c) Compute a 99% confidence interval for the population mean? of home run percentages for all professional baseballplayers. (Round your answers to two decimal places.)
| lower limit | % |
| upper limit | % |
(d) The home run percentages for three professional players arebelow.
| Player A, 2.5 | Player B, 2.3 | Player C, 3.8 |
Examine your confidence intervals and describe how the home runpercentages for these players compare to the populationaverage.
We can say Player A falls close to the average, Player B isabove average, and Player C is below average.
We can say Player A falls close to the average, Player B isbelow average, and Player C is aboveaverage.
We can say Player A and Player B fall close to the average,while Player C is above average.
We can say Player A and Player B fall close to the average,while Player C is below average.
(e) In previous problems, we assumed the x distributionwas normal or approximately normal. Do we need to make such anassumption in this problem? Why or why not? Hint: Use thecentral limit theorem.
Yes. According to the central limit theorem, when n ?30, the x distribution is approximately normal.
Yes. According to the central limit theorem, when n ?30, the x distribution is approximatelynormal.
No. According to the central limit theorem, when n ?30, the x distribution is approximately normal.
No. According to the central limit theorem, when n ?30, the x distribution is approximately normal.
