The mean height of 50 male students who showed above-average participation in college athletics

was 173.3 cm with s.d. 6.4 cm, while 50 male students who showed no interest in such

participation had a mean of 171.5 cm and s.d. 7.1 cm. Test the hypothesis that male students who

participate in college athletics are taller than other students at 5% level of significance using

sample s.d. as an estimate of population s.d. By how much the sample size of each group should

be increased in order that the observed difference of 1.8 cm in the mean heights is significant at

the same level of significance.