Question

Difference in proportions --

A Gallup poll of 1240 randomly-selected teens conducted in 2001 found that boys were more likely than girls to play video games, by a margin of 57% to 35%. If an equal number of boys and girls were surveyed, test an appropriate hypothesis to tell whether there’s enough evidence to claim that boys play video games more than girls.

Answer 1

For Boys:

n1 = 620, p̂1 = 0.57

For girls:

n2 = 620, p̂2 = 0.35

α = 0.05

Null and Alternative hypothesis:

Ho : p1 = p2 ; H1 : p1 > p2

Pooled proportion:

p̄ = (n1*p̂1+n2*p̂2)/(n1+n2) = (353.4+217)/(620+620) = 0.46

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.57 - 0.35)/√[0.46*0.54*(1/620+1/620)] = 7.7719

p-value = 1- NORM.S.DIST(7.7719, 1) = 0.0000

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that there is enough evidence to claim that boys play video games more than girls.