A random sample has mean height of 80 boys who participated

A random sample has mean height of 80 boys, who participated in the athletic competition was 167 cm with a standard deviation of 9 cm. The mean height of the 160 boys who did not participate in the athletic competition was 163 cm with a standard deviation of 10 cm. test the hypothesis at 5% level of significance, whether the boys who participate in athletics are taller than the other.

Solution

H0:mu1=mu2

H1:mu1>mu2

The test statistics is z=(X1bar-x2bar)/(s1^2/n1+s2^2/n2)=5.47

It is right tailed test. Given alpha =0.05, the critical z value is

1.645. Since z=5.47 is greater than z critical value 1.645. We reject H0.

So we conclude the boy who participates in athletic are taller than others.