For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 3.31. 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.

1 month agoTest Statistic = 3.31 Find the area under the standard normal Z curve, which is to the left of z = 3.31 to get this approximate result P(Z < 3.31) = 0.9995 I used this Z table http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf scroll to the second page, then locate the row that starts with "3.3" and the column that has 0.01 at the top. The value 0.9995 is in this row and column combination Since P(Z < 3.31) = 0.9995 this means, P(Z > 3.31) = 1-P(Z < 3.31) P(Z > 3.31) = 1 - 0.9995 P(Z > 3.31) = 0.0005 The chances of getting a Z value that is beyond 3.31 is very small Double this to get 2*0.0005 = 0.001 We double this area due to the fact that we have a two tailed hypothesis test Therefore the p value is approximately 0.001 This p value is smaller than alpha = 0.05 and alpha = 0.01 So that's why the answer is A) The result is significant at both a = 0.05 and a = 0.01 meaning we reject the null hypothesis at either alpha level and favor the alternative which says that \(\large p_1 - p_2 \ne 0\). This can be rewritten into \(\large p_1 \ne p_2\) (ie the population proportions of the two groups are likely to be different)

1 month ago