Is there a relationship between confidence intervals andtwo-tailed hypothesis tests? Let c be the level of confidence usedto construct a confidence interval from sample data. Let α be thelevel of significance for a two-tailed hypothesis test. Thefollowing statement applies to hypothesis tests of the mean. For atwo-tailed hypothesis test with level of significance α and nullhypothesis H0: μ = k, we reject H0 whenever k falls outside the c =1 − α confidence interval for μ based on the sample data. When kfalls within the c = 1 − α confidence interval, we do not rejectH0. (A corresponding relationship between confidence intervals andtwo-tailed hypothesis tests also is valid for other parameters,such as p, μ1 − μ2, or p1 − p2, which we will study later.)Whenever the value of k given in the null hypothesis falls outsidethe c = 1 − α confidence interval for the parameter, we reject H0.For example, consider a two-tailed hypothesis test with α = 0.01and H0: μ = 20 H1: μ ≠ 20

A random sample of size 30 has a sample mean x = 23 from apopulation with standard deviation σ = 6.

(a) What is the value of c = 1 − α? 2.826 Incorrect: Your answeris incorrect.

Construct a 1 − α confidence interval for μ from the sampledata. (Round your answers to two decimal places.)

lower limit

upper limit

What is the value of μ given in the null hypothesis (i.e., whatis k)? k = Is this value in the confidence interval?

Yes No Correct: Your answer is correct. Do we reject or fail toreject H0 based on this information? We fail to reject the nullhypothesis since μ = 20 is not contained in this interval. We failto reject the null hypothesis since μ = 20 is contained in thisinterval. We reject the null hypothesis since μ = 20 is notcontained in this interval. We reject the null hypothesis since μ =20 is contained in this interval. Correct: Your answer iscorrect.

(b) Using methods of this chapter, find the P-value for thehypothesis test. (Round your answer to four decimal places.)