Question

We have created a 99​% confidence interval for μ with the result ​(11​,16​). What conclusion will we make if we test H₀: μ = 19 vs. Hₐ: μ ≠ 19 at α = 0.01?

A. Reject H₀ in favor of Hₐ.

B.Accept H₀ rather than Hₐ.

C.Fail to reject H₀.

D. We cannot tell what our decision will be with the information given.

Answer 1

The value 19 does not fall within the 99% confidence interval (11, 16), so at the 0.01 significance level, the null hypothesis H₀: μ = 19 is rejected in favor of the alternative hypothesis Hₐ: μ ≠ 19.

Step-by-step explanation:

You have created a 99% confidence interval for μ (mu), which is the mean of a population, and the interval is (11, 16). If you are testing the null hypothesis H0: μ = 19 against the alternative hypothesis Ha: μ ≠ 19 at an alpha level of 0.01, you can make your decision based on whether the hypothesized value of 19 falls inside or outside of the confidence interval.

Since 19 is not within the interval (11, 16), you can conclude that the value of μ is significantly different from 19 at the 1% significance level. Thus, you would reject the null hypothesis in favor of the alternative hypothesis.

This is because your confidence interval does not encompass the value of μ that the null hypothesis claims it should be, which implies there is less than a 1% chance that this difference is due to random variation. Therefore, the correct choice is A. Reject H0 in favor of Ha.