Question

For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

The result is significant at both α = 0.05 and α = 0.01.
The result is significant at α = 0.05 but not at α = 0.01.
The result is significant at α = 0.01 but not at α = 0.05.
The result is not significant at either α = 0.05 or α = 0.01.
The result is inconclusive because we don't know the value of p.

Answer 1

What do you think it is? I will eliminate the last option "inconclusive" because from what I know of statistics, we have enough data to determine where this result is significant at. We must convert this Test Statistic into a P-Value and if the P-Value is greater than 0.01 (alpha), we say it is "significant at 0.01" and if it's also greater at 0.05 (alpha), we say it is "significant at 0.05 and 0.01" I believe. I verified as much as I could with research. We are finding "does not equal" so it is a two-proportions test" meaning that the test statistic probability must be greater than two times the z-table probability value. When z = 1.8, P(z ≠ 1.8) is 0.0359. Multiply this by two as I believe, then this p-value will be 0.0718, which leads me to believe the answer is the First Option that it is significant at 0.01 & 0.05. I ask you to submit this answer and let me know if I was correct in believing so as I would like to know if I was correct myself. Hope I helped.