Question

pA researcher at UAEU recently sampled 250 families from Al-Ain and determined that 160 of them have internet connection at home. A similar poll of 200 families carried out in year 2000 yielded a total of 70 families having internet connection at home. Do these figures prove that the proportion of houses with internet connection has increased since 2000? Use the 5% level of significance.

Answer 1

Given:

X1 = 160 , n1 = 250

X2 = 70 , n2 = 200

Sample proportion :

1 = X1/n1 = 160/250 = 0.64

2 = X2/n2 = 70/200 = 0.35

Pooled proportion :

= X1+X2/n1+n2 = (160+70)/250+200 = 0.5111

Claim : The proportion of houses with internet connection has increased since 2000.

Hypothesis test:

The null and alternative hypothesis is

Ho : p1- p2 = 0

Ha : p1 - p2 > 0

Decision : Reject null hypothesis.

Conclusion : There is sufficient evidence to conclude that the proportion of houses with internet connection has increased since 2000 at 0.05 significance level.