Question

The mean height of 50 Male students who showed above average participation in college athletics was 68.2 inches with a sd of 2.5 inches, while 50 students who showed no interest in such participation had a mean height of 67.5 inches with a standard deviation of 2.8 inches. Test the hyphothesis that male students who participate in college athletics are taller than the other male students at 0.05 level of significance

Answer 1

Solution

Let students participating in athletics be rep. by 1 while those not participating by 2.

$H_0 :\mu_1 = \mu_2$ Vs $H_1: \mu_1 > \mu_2$

Test statistic :

$$(\bar{x_1} - \bar{x_2}) - (\mu_1 - \mu_2) \over \sqrt{ { s^2_1 \over {n_1}}+{s^2_2 \over n_2}}$$

$$={(68.2-67.5)-0 \over \sqrt{ {2.5^2 \over 50} +{2.8^2 \over 50} }} =1.3715$$

Z-score :

$Z_{0.95}=1.645$

Since z-tab > z-calculated, we fail to reject the null hypothesis. Thus we conclude that there is no significant difference between the height of students participating in athletics and those not participating in athletics