Question: For the following data, test the claim that \({{p}_{1}}={{p}_{2}}\), at the 0.05 significance level.

Low High

n₁ = 5239 n₂ = 4939

x₁ = 52 x₂ = 25

(a) State the null and alternative hypotheses

(b) Calculate \({{\hat{p}}_{1}}\) and \({{\hat{p}}_{2}}\)

(c) Find the pooled estimate \(\bar{p}\)

(d) Find the z-statistics

(e) Find the critical z-value

(f) Find the p-value

(g) State the conclusion

(h) Construct a 90% confidence interval estimate for the difference between the two proportions

(i) Does the confidence interval estimate agree with your conclusion? Explain why?

(j) Does the confidence interval estimate always result in the same conclusion as the hypothesis test? Explain why or why not.