Question

A survey of high school girls classified them by two attributes: whether or not they participated in sports and whether or not they had one or more older brothers. Use the following data to test the null hypothesis that these two attributes of classification are independent:

Answer 1

From hypothesis, there is sufficient evidence to conclude that there is significant difference in two proportions.

Explanation:

sample proportion for 1=12/20=0.6

sample proportion for 2=13/40=0.325

pooled proportion=25/60=0.4167

Test statistic:

z=(0.6-0.325)/sqrt(0.4167*(1-0.4167)*((1/20)+(1/40)))

z=2.037

p-value=2*P(z>2.037)=0.0417

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that there is significant difference in two proportions.