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 test statistic approach, what conclusion should be reached about the null hypothesis? A) Because z = 2.40 1.96, we reject the null hypothesis. B) Because z = 2.03 1.96, we reject the null hypothesis. C) Because z = 1.78

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 test statistic approach, what conclusion should be reached about the null hypothesis? A) Because z = 2.40 > 1.96, we reject the null hypothesis. B) Because z = 2.03 > 1.96, we reject the null hypothesis. C) Because z = 1.78 < 1.96, we do not reject the null hypothesis. D) Because z = 1.45 < 1.645, we do not reject the null hypothesis.

Quizplus · Accepted Answer

The correct conclusion is based on comparing the computed test statistic (z = 1.78) with the critical value for a two-tailed test at the alpha level of 0.05, which is 1.96. Since 1.78 is less than 1.96, we do not reject the null hypothesis.

A Decision Maker Wishes to Test the Following Null and Alternative