Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let e be the level of confidence used to construct a confidence interval from sample data. Let αα be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean. (A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters such as p, ', or , which we will study in Section 9.3, 10.2, and 10.3.) Whenever the value of k given in the null hypothesis falls outside the c=1−α confidence interval for the parameter, we reject . For example, consider a two-tailed hypothesis test with \alpha =0.01 and sample mean x¯=22 from a population with standard deviation σ=4.
(a) What is the value of c=1−α. Using the methods, construct a 1−α confidence interval for μ from the sample data. What is the value of μ given in the null hypothesis (i.e., what is k)? Is this value in the confidence interval? Do we reject or fail to reject H0 based on this information?
(b) using methods, find the P-value for the hypothesis test. Do we reject or fail to reject ? Compare your result to that of part (a).