# Question: The following relationship holds between hypothesis tests and confidence intervals

The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis Ha: μ = μ0 if and only if μ0 lies outside the (1 − α)-level confidence interval for μ.

In each case, illustrate the preceding relationship by obtaining the appropriate one-mean t-interval (Procedure 8.2 on page 328) and comparing the result to the conclusion of the hypothesis test in the specified exercise.

a. Exercise 9.101

b. Exercise 9.104

In each case, illustrate the preceding relationship by obtaining the appropriate one-mean t-interval (Procedure 8.2 on page 328) and comparing the result to the conclusion of the hypothesis test in the specified exercise.

a. Exercise 9.101

b. Exercise 9.104

## Answer to relevant Questions

In Exercise 8.113 on page 335, we introduced one-sided one-mean t-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a left-tailed hypothesis test at ...Suppose that, in a hypothesis test, the null hypothesis is in fact false. a. Is it possible to make a Type I error? Explain your answer. b. Is it possible to make a Type II error? Explain your answer. Refer to Exercise 9.9. Explain what each of the following would mean. a. Type I error b. Type II error c. Correct decision Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null ...Explain in your own words the meaning of each of the following terms. a. Test statistic b. Rejection region c. Nonrejection region d. Critical values e. Significance level A right-tailed test with α = 0.05. Determine the critical value(s) for a one-mean z-test. For each exercise, draw a graph that illustrates your answer.Post your question