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, 2.4 |
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, whenn
≤ 30, the distribution is approximately normal.
No. According to the central limit theorem, whenn
≥ 30, the distribution is approximately normal.
No. According to the central limit theorem, whenn
≤ 30, the distribution is approximately normal.