A decision maker wishes to test the following null and alternative hypotheses using an alpha level equal to 0.05: H₀ : μ₁ - μ₂ = 0
H_A : 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?

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 H_A : 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

Since the alpha level is 0.05, our critical value for a two-tailed test is 1.96. Our test statistic is 1.78, which falls within the acceptance region between -1.96 and 1.96. Therefore, we do not reject the null hypothesis.

A Decision Maker Wishes to Test the Following Null and Alternative