Question

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : p 1 = p 2 H a : p 1 ≠ p 2 You obtain 83.1% successes in a sample of size n 1 = 688 from the first population. You obtain 86.6% successes in a sample of size n 2 = 749 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion. There is not sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion. The sample data support the claim that the first population proportion is not equal to the second population proprtion. There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proprtion.

Answer 1

Given that,

For sample 1 :

For sample 2 :

The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

Pooled proportion is,

Test statistic is,

=> Test statistic = -1.852

p-value = 2 * P(Z < -1.852) = 2 * 0.0320 = 0.0640

=> p-value = 0.0640

​​​​​The p-value is greater than α This test statistic leads to a decision to fail to reject the null.

As such, the final conclusion is that, There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proportion.