Question

AL baseball teams play with a designated hitter, meaning the pitchers don’t bat. The league believes that replacing the pitcher, typically a weak hitter, with another player produces more runs and generates more interest among fans. Below are the average numbers of runs scored in AL and NL stadiums for the 2006 season.

American League:

11.4, 10.5, 10.4, 10.3, 10.2, 10.0, 9.9, 9.9, 9.7, 9.1, 9.0, 9.0, 8.9, 8.8

National League:

10.5, 10.3, 10.0, 10.0, 9.7, 9.7, 9.6, 9.5, 9.5, 9.4, 9.1, 9.0, 9.0, 8.9, 8.9, 7.9

a. With a 99% confidence interval, estimate the mean number of runs scored in AL games.

b. Coors Field, in Denver, stands a mile above sea level, and some believe the thinner air makes it harder for pitchers to throw curve balls and easier for batters to hit the ball far. Do you think the 10.5 runs scored per game at Coors Field is unusual? Explain.

Answer 1

Following table shows the descriptive statistics of both data set:

Descriptive statistics
	AL	NL
count	14	16
mean	9.793	9.438
sample standard deviation	0.758	0.639
sample variance	0.575	0.408
minimum	8.8	7.9
maximum	11.4	10.5
range	2.6	2.6

a)

Here we have

Since there 14 data values in the sample so degree of freedom is df=14-1=13 and critical value of t for 99% confidence interval, using excel function "=TINV(0.01,13)" is 3.012.

The required confidence interval is

b)

Here we have

Since there 16 data values in the sample so degree of freedom is df=16-1=15 and critical value of t for 99% confidence interval, using excel function "=TINV(0.01,15)" is 2.947.

The required confidence interval is

Since 10.5 does not lie in the above interval so it is unusual that the 10.5 runs scored per game at Coors Field .