Question

Batting Averages Random samples of batting averages from the leaders in both leagues prior to the All-Star break are shown. At the 0.01 level of significance, can a difference be concluded?

National 0.311 0.328 0.324 0.338 0.326

American 0.348 0.325 0.352 0.321 0.333

Compute the test value. Always round t- score value to three decimal places. Do not round intermediate steps.

Reject or do not reject the null hypothesis.

There is or is not enough evidence to support the claim?

Answer 1

Null Hypothesis H0: The batting averages from the leaders in National and American leagues are equal.

Alternative Hypothesis H1: The batting averages from the leaders in National and American leagues are not equal.

As, the same people are playing in both the leagues, this is a matched pair design and we will use matched pair t test.

The difference in batting averages are,

-0.037, 0.003, -0.028, 0.017, -0.007

Mean difference, = -0.0104

Standard deviation of difference = 0.02213143

Standard error of mean differences = 0.02213143 / = 0.009897476

test value t = / Std Error = -0.0104 / 0.009897476 = -1.051

Degree of freedom = n-1 = 5-1 = 4

For two tail test, P-value = 2 * P(t < -1.051) =  0.3526

Since, p-value is greater than 0.01 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence to support the claim that batting averages from the leaders in both leagues are different.