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...

Extracted text: 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 Họ: H = k, we reject Ho whenever k falls outside the c = 1- a confidence interval for u based on the sample data. When k falls within the c = 1 - a confidence interval, we do not reject Ho.- (A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, u, – H2, or p1 - P2, which we will study in later sections.) Whenever the value of k given in the null hypothesis falls outside the c = 1- a confidence interval for the parameter, we reject Hg. For example, consider a two-tailed hypothesis test with a = 0.01 and Ho: H = 21 Hị: u = 21 A random sample of size 19 has a sample mean x = 22 from a population with standard deviation o = 5. (a) What is the value of c = 1 - a? Using the methods of Chapter 7, construct a 1 - a confidence interval for u from the sample data. (Round your answers to two decimal places.) lower limit upper limit What is the value of u given in the null 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 Fail to reject, since u = 21 is not contained in this interval. O Fail to reject, since u = 21 is contained in this interval. Reject, since u = 21 is not contained in this interval. O Reject, since u = 21 is contained in this interval. (b) Using methods of Chapter 8, find the P-value for the hypothesis test. (Round your answer to four decimal places.) Do we reject or fail to reject Ho? O Reject the null hypothesis, there is sufficient evidence that µ differs from 21. O Fail to reject the null hypothesis, there is insufficient evidence that u differs from 21. O Fail to reject the null hypothesis, there is sufficient evidence that u differs from 21. O Reject the null hypothesis, there is insufficient evidence that u differs from 21. 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). These results are the same.