Question

A random sample of 32 baseball players and a random sample of 27 soccer player were obtained and each player was weighed in pounds. The mean weight of the baseball players is 186 pounds with a standard deviation of 10.1 pounds. The mean weight of the soccer players is 168 pounds with a standard deviation of 3.0 pounds. Use a significance level of .05 to test the claim that the mean weight of baseball players is the same as the mean weight of the soccer players by completing a hypothesis test. Let the sample of baseball players be sample 1 and the sample of soccer players be sample 2.

Answer 1

First we check whether two samples have equal variance or not.

Test statistic,

It has (n1-1, n2-1) = (31,26) degrees of freedom.

Critical value = F31,26 = 1.89

Since calculated value is greater than critical value we reject null hypothesis and conclude that two samples have significantly different variances.

Hypothesis:

Test statistic,

Degrees of freedom:

Critical value = t37,0.05/2 = 2.026

Since calculated value of t is greater than critical value we reject null hypothesis and conclude that the mean weight of baseball players is not same as the mean weight of the soccer players at 5% level of significance.