Question

(1)

A study of 30 Major League baseball teams investigates whether more strikouts in nine innings tends to be correlated with fewer walks and hits per inning . Consider the hypotheses:

The sample correlation between number of strikeouts in nine innings and the number of walks and hits per inning is r = -0.594 and the p-value is 0.036.

At what value would the Bootstrap Distribution for correlation be centered?

		-0.594
		0.036
		30
		0

(2)

A study of 30 Major League baseball teams investigates whether more strikouts in nine innings tends to be correlated with fewer walks and hits per inning. Consider the hypotheses: :

The sample correlation between number of strikouts in nine innings and number of walks and hits per inning is r = -0.594 and the p-value is 0.036.

Choose the correct interpretation of the p-value.

		Assuming there is no correlation between strikouts in nine innings and walks and hits per inning the chance of observing this sample correlation or one even more extreme is 0.036.
		There is a 0.036 chance that there is a negative association between strikouts in nine innings and walks and hits per inning .
		Assuming there is strong evidence of a negative correlation between strikouts in nine innings and walks and hits per inning, the chance of observing this sample correlation or one even more extreme is 0.036.

(3)

A study of 30 Major League baseball teams investigates whether more strikouts in nine innings tends to be correlated with fewer walks and hits per inning. Consider the hypotheses: :

The sample correlation between number of strikouts in nine innings and number of walks and hits per inning is r = -0.594 and the p-value is 0.036.

Indicate the formal statistical decision at a significance level of  .

		Reject
		Fail to reject

(4)

A study of 30 Major League baseball teams investigates whether more strikouts in nine innings tends to be correlated with fewer walks and hits per inning. Consider the hypotheses: :

The sample correlation between number of strikouts in nine innings and number of walks and hits per inning is r = -0.594 and the p-value is 0.036.

Now consider the test with a two-tailed alternative:

Write a "statistical significance" conclusion for this two-tailed test, being sure to include the two-sided p-value.   Use a 10% significance level.

Answer 1

1)

The bootstrap distribution is centered around the sample statistic

= -0.594

option a) is correct

2)

Assuming there is no correlation between strikouts in nine innings and walks and hits per inning the chance of observing this sample correlation or one even more extreme is 0.036.

3)

since p-value = 0.036 < alpha (0.05)

we reject the null

4)

p-value for 2-tailed = 2 * 0.036 = 0.072

since p-value < alpha

we reject the null hypothesis

we conclude that there is significant correlation between two variables