Question

You wish to test the following claim ( H a ) at a significance level of α = 0.001 . H o : p 1 = p 2 H a : p 1 < p 2 You obtain 167 successes in a sample of size n 1 = 306 from the first population. You obtain 436 successes in a sample of size n 2 = 736 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 =

Answer 1

Here we can use ti-83 calculator .

step : STAT -> TESTS - 2 Prop Z test -> Stats

Test Hypothesis :

H0: p1 = p2

Ha: p1 < p2

Test statistic :

Z = -1.389

P-value :

P = 0.0825

Conclusion :

P-value greater than alpha = 0.001 then conclude that fail to reject H0.