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 1.71.3 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 0.01.8 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 bar and s (in percentages). (For each answer, enter anumber. Round your answers to two decimal places.) x bar = x bar =% s = %
(b) Compute a 90% confidence interval (in percentages) for thepopulation mean ? of home run percentages for all professionalbaseball players. Hint: If you use the Student's t distributiontable, be sure to use the closest d.f. that is smaller. (For eachanswer, enter a number. Round your answers to two decimal places.)lower limit % upper limit %
(c) Compute a 99% confidence interval (in percentages) for thepopulation mean ? of home run percentages for all professionalbaseball players. (For each answer, enter a number. Round youranswers to two decimal places.) lower limit % upper limit %
(d) The home run percentages for three professional players arebelow. Player A, 2.5 Player B, 2.2 Player C, 3.8 Examine yourconfidence intervals and describe how the home run percentages forthese players compare to the population average.
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 above average.
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 distribution wasnormal or approximately normal. Do we need to make such anassumption in this problem? Why or why not? Hint: Use the centrallimit theorem.
Yes. According to the central limit theorem, when n ? 30, the xbar distribution is approximately normal.
Yes. According to the central limit theorem, when n ? 30, the xbar distribution is approximately normal.
No. According to the central limit theorem, when n ? 30, the xbar distribution is approximately normal.
No. According to the central limit theorem, when n ? 30, the xbar distribution is approximately normal.
