Question

Given two independent random samples with the following results:

n1=562      x1 =273

???n2=356    x2=144

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

for the test.

1. Compute the weighted estimate of p, p??. Round your answer to three decimal places.

2. Compute the value of the test statistic. Round your answer to two decimal places.

3. Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to two decimal places.

Answer 1

Null Hypothesis H0: p1=p2

ALternative Hypothesis

Under null hypothesis, the test statistic

The proportion p1 = x1/n1 = 273/562 =0.486

The proportion p2 = x2/n2 = 144/356 =0.404

1) The weighted estimate of p is

2) The test statistic is

3) The critical value of Z for two tailed test and at 5% significance level is 1.96

Decision Rule : Reject H0 if Z<-1.96 or Z>1.96

Since Z calculated is greater than Z tabulated, Reject H0.

Hence we have enough evidence to conclude that there is a difference between the two population proportions