Question

Given two independent random samples with the following results:

n1=428 x1=270   n2=251 x2=135

Can it be concluded that there is a difference between the two population proportions? Use a significance level of α=0.05 for the test.

Step 1 of 6: State the null and alternative hypotheses for the test

Step 2 of 6: Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 3 of 6: Compute the weighted estimate of p, p‾. Round your answer to three decimal places.

Step 4 of 6: Compute the value of the test statistic. Round your answer to two decimal places.

Step 5 of 6: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places

Step 6 of 6: Make the decision for the hypothesis test

Answer 1

Step 1 of 6 : The and alternative hypothesis is ,

Step 2 of 6 :

Step 13of 6 :

Step 4 of 6 :

Step 5 of 6 : The critical value is ,

; From Z-table

Decision rule : reject Hi , if Z-stat>1.96 or Z-stat<-1.96

Here , Z-stat=2.38>1.96

Therefore , reject Ho.

Step 6 of 6 : Conclusion : There is sufficient evidence to concluded that there is a difference between the two population proportions.