Question

Suppose that we have hypotheses H₀:μ=μ₀ vs H₁:μ=μ₀ , and we conduct a test with a significance level 0.05 . Which following is correct?

a.If we reject the null hypothesis from the test, the corresponding 95% confidence interval for μ will contain μ₀.
b.If we fail to reject the null hypothesis from the test, we will obtain the same result even with the significance level 0.01 .
c.If we find that 95% confidence interval for μ does not include μ₀, we will reach to the conclusion of failing to reject the null hypothesis from the test.
d.If we made a decision to support the alternative hypothesis from the test, it implies that we observed p-value >0.05.

Answer 1

The correct answer is c. If we find that 95% confidence interval for μ does not include μ₀, we will reach the conclusion of failing to reject the null hypothesis from the test.

Step-by-step explanation:

The correct answer is c. If we find that 95% confidence interval for μ does not include μ₀, we will reach the conclusion of failing to reject the null hypothesis from the test.

When conducting a hypothesis test, we reject the null hypothesis if the p-value is less than the significance level (in this case, 0.05). However, if the 95% confidence interval for μ does not include the hypothesized value μ₀, it means that μ₀ is not a likely estimate for the population mean μ, supporting the alternative hypothesis that μ≠μ₀ or μ>μ₀.