The home run percentage is the number of home runs per 100 times at bat. A rando

Question

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 x and s. (Round your answers to two decimal places.)

(b) Compute a 90% confidence interval for the population mean 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. (Round your answers to two decimal places.)

(c) Compute a 99% confidence interval for the population mean of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

(d) The home run percentages for three professional players are below.

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, when n 30, the x distribution is approximately normal. Yes. 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. No. According to the central limit theorem, when n 30, the x distribution is approximately normal.

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

Explanation / Answer

SolutionA:

Rcode:

Runs1 <- c(1.6,2.4, 1.2, 6.6, 2.3, 0, 1.8, 2.5, 6.5, 1.8, 2.7, 2, 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, 4.1,

2.9, 1.9, 2.4, 0, 1.8, 3.1, 3.8, 3.2, 1.6, 4.2, 0, 1.2, 1.8, 2.4)

mean(Runs1)

sd(Runs1)

output:

> mean(Runs1)
[1] 2.293023
> sd(Runs1)
[1] 1.401087

Answers:

mean=2.29

sd=s=1.40

Solutionb:

t.test(Runs1,conf.level=0.90)

output:

One Sample t-test

data: Runs1

t = 10.732, df = 42, p-value = 1.306e-13

alternative hypothesis: true mean is not equal to 0

90 percent confidence interval:

1.933651 2.652396

sample estimates:

mean of x

2.293023

ANSWER:

90 percent confidence interval:

1.93 and 2.65

Solutionc:

t.test(Runs1,conf.level=0.99)

Output:

One Sample t-test

data: Runs1
t = 10.732, df = 42, p-value = 1.306e-13
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
1.716544 2.869502
sample estimates:
mean of x
2.293023

ANSWERS:

99 percent confidence interval:
1.72 and 2.87

Solutiond:

90 percent confidence interval:

1.93 and 2.65

99 percent confidence interval:
1.72 and 2.87

We can say Player A and Player B fall close to the average, while Player C is above average.

Player C, 3.8

Player A, 2.5(Falls in 99% CI) Player B, 1.9(Falls in 99% CI)

Player C, 3.8

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