A decision maker wishes to test the following null and alternative hypotheses using an alpha level equal to 0.05: H0 : μ1 - μ2 = 0 HA : μ1 - μ2 ≠ 0 The population standard deviations are assumed to be known. After collecting the sample data, the test statistic is computed to be z = 1.78 Using the p-value approach, what decision should be reached about the null hypothesis? A) Since p-value = 0.0018 α/2 = 0.025, do not reject the null hypothesis. C) Since p-value = 0.0033 α/2 = 0.025, do not reject the null hypothesis.

Question

A decision maker wishes to test the following null and alternative hypotheses using an alpha level equal to 0.05: H0 : μ1 - μ2 = 0 HA : μ1 - μ2 ≠ 0 The population standard deviations are assumed to be known. After collecting the sample data, the test statistic is computed to be z = 1.78 Using the p-value approach, what decision should be reached about the null hypothesis? A) Since p-value = 0.0018 < α/2 = 0.025, reject the null hypothesis B) Since p-value = 0.0415 > α/2 = 0.025, do not reject the null hypothesis. C) Since p-value = 0.0033 < α/2 = 0.025, reject the null hypothesis. D) Since p-value = 0.0375 > α/2 = 0.025, do not reject the null hypothesis.

Quizplus · Accepted Answer

The p-value for a z-score of 1.78 in a two-tailed test is greater than 0.05 but less than 0.10, specifically around 0.075. Since we are conducting a two-tailed test at α = 0.05, we compare the p-value to α/2 = 0.025. The correct interpretation is that since the p-value is greater than α/2, we do not reject the null hypothesis. None of the provided p-values exactly match the correct p-value for a z-score of 1.78, but option D's logic of not rejecting the null hypothesis due to the p-value being greater than α/2 is the correct approach, despite the specific p-value provided being incorrect.

A Decision Maker Wishes to Test the Following Null and Alternative