Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let a be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean. For a two-tailed hypothesis test with level of significance a and null hypothesis Hg: -k, we reject H, whenever k falls outside the c-1-a confidence interval for u based on the sample data, When k falls within the c1-a confidence interval, we do not reject H (A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, , - a, or p, - Pa, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the e-1-a confidence interval for the parameter, we reject H. For example, consider a two-tailed hypothesis test with e 0.01 and Me:- 20 A random sample of size 38 has a sample mean x- 23 from a population with standard deviation e- 5. H 20 (a) What is the value of e -1- a? Construct a 1 - a confidence interval for a from the sample data. (Round your answers to two decimal places.) lower limit upper limit What is the value of a given in the nul hypothesis (i.e., what is k)? k- Is this value in the confidence interval? O Yes O No Do we reject or fail to reject H, based on this information? O We fail to reject the null hypothesis since - 20 is not contained in this interval. O we fail to reject the null hypothesis since - 20 is contained in this interval. O We reject the null hypothesis since a- 20 is not contained in this interval. O we reject the null hypothesis since u 20 is contained in this interval. (b) Using methods of this chapter, find the Pvalue for the hypothesis test. (Round your answer to four decimal places.) Do we reject or fail to reject H,? O we fail to reject the null hypothesis since there is sufficient evidence that a differs from 20. O we fail to reject the null hypothesis since there is insufficient evidence that differs from 20. O we reject the null hypothesis since there is sufficient evidence that differs from 20. O we reject the null hypothesis since there is insufficient evidence that a differs from 20. Compare your result to that of part (a). O we rejected the null hypothesis in part (b) but failed to reject the null hypothesis in part (a). O we rejected the null hypothesis in part (a) but failed to reject the null hypothesis in part (b). O These results are the same.

Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let ? 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, ?₁ − ?₂, or p₁ − p₂, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the c = 1 − ? confidence interval for the parameter, we reject H₀. For example, consider a two-tailed hypothesis test with ? = 0.01 and

A random sample of size 38 has a sample mean x = 23 from a population with standard deviation ? = 5.