Hypothesis testing and confidence interval for two proportions:

In a study to estimate the proportion of housewives who own IPods, it is found that 120 out of 200 suburban residents and 240 out of 500 urban residents own IPods.

a) Is there a significant difference between the proportion of suburban and urban housewives who own IPods? Use α = 0.04.

b) Establish a 99% confidence interval for the difference in the proportion of suburban and urban housewives who own IPod.

c) Estimate the type II (β) if the alternative hypothesis is:

i)two-sided, i.e.: p₁ ¹  p_2, with α = 0.01
ii)one-sided, i.e.: p₁ > p_2, with α = 0.05
iii)one-sided, i.e.: p₁ < p₂, with α = 0.025

d) Compute the common sample size for the two sided alternative hypotheses in part (c)