Is there a relationship between confidence Intervals and two-talled hypothesis tests? Let c be the level of confidence used to construct a c of the mean. e Interval from sample data. Let of be the level of significance for a two-talled hypothesis test. The following statement applies to hypothesis tests For a two-talled hypothesis test with level of significance of and null hypothesis Hol = k, we reject Ho whenever k falls outside the c = 1 - a confidence Interval for 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-talled hypothesis tests also Is valid for other parameters, such as p, H, - 2, or P, - 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 Ho. For example, consider a two-talled hypothesis test with a = 0.01 and Hot H = 21 Hill - 21 A random sample of size 20 has a sample mean x = 23 from a population with standard deviation o = 4. (a) What is the value of c = 1 - 037 Using the methods of Chapter 7, construct a 1 - of 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 (L.e., what Is k) ? K = Is this value in the confidence Interval? Yes O NO Do we reject or fall to reject Ho based on this Information? O Fail to reject, since ( = 21 Is not contained in this Interval, O Fall to reject, since if = 21 Is contained in this interval, O Reject, since LI = 21 is not contained in this Interval . Reject, since if = 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 fall to reject Ho? O Reject the null hypothesis, there is sufficient evidence that u differs from 21 O Fail to reject the null hypothesis, there is Insufficient evidence that i differs from 21. A O US 1 7 8 10:15 O