Question

Given two independent random samples with the following results:

n1= 658    n2 = 550

x1=362      x2=194

Can it be concluded that there is a difference between the two population proportions? Use a significance level of α=0.01 for the test.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 3 of 5: Compute the weighted estimate of p, p‾. Round your answer to three decimal places.

Step 4 of 5: Compute the value of the test statistic. Round your answer to two decimal places.

Step 5 of 5: Find the P-value for the hypothesis test. Round your answer to four decimal places.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Fail to reject the null hypothesis. There is sufficient evidence, at the 0.01 level of significance, that there is a difference between the two population proportions.

Fail to reject the null hypothesis. There is not sufficient evidence, at the 0.01 level of significance, that there is a difference between the two population proportions.

Reject the null hypothesis. There is sufficient evidence, at the 0.01 level of significance, that there is a difference between the two population proportions.

Reject the null hypothesis. There is not sufficient evidence, at the 0.01 level of significance, that there is a difference between the two population proportions.

Answer 1

Step 1) The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

Step 2) sample proportion 1 = 362/658 = 0.550

sample proportion 2 = 194/550 = 0.353

Step 3) Weighted estimtae of p is,

Step 4) Test statistic is,

=> Test statistic = Z = 6.84

Step 5) p-value = 2 * P(Z > 6.84) = 2 * 0.0000 = 0.0000

=> p-value = 0.0000

Step 6) Since, p-value < 0.01

=> Reject the null hypothesis. There is sufficient evidence, at the 0.01 level of significance, that there is a difference between the two population proportions.