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.
(a)
Use a calculator with mean and standard deviation keys to find and
s (in percentages). (For each answer, enter a number. Round your answers to two decimal places.)
= x bar = %
s = %
(b)
Compute a 90% confidence interval (in percentages) 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. (For each answer, enter a number. Round your answers to two decimal places.)
lower limit %
upper limit %
(c)
Compute a 99% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. (For each answer, enter a number. Round your answers to two decimal places.)
lower limit %
upper limit %
(d)
The home run percentages for three professional players are below.
Player A, 2.5 |
Player B, 2.0 |
Player C, 3.8 |
Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.
We can say Player A falls close to the average, Player B is above average, and Player C is below average. We can say Player A falls close to the average, Player B is below 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 was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not?
Hint: Use the central limit theorem.
Yes. According to the central limit theorem, whenn
≥ 30, the distribution is approximately normal. Yes. According to the central limit theorem, when
n
≤ 30, the distribution is approximately normal. No. According to the central limit theorem, when
n
≥ 30, the distribution is approximately normal.No. According to the central limit theorem, when
n
≤ 30, the distribution is approximately normal.