Expand Your Knowledge: Confi dence Intervals and Two-Tailed Hypothesis Tests Is there a relationship between confi dence intervals and two-tailed hypothesis tests? Let c be the level of confi dence used to construct a confi dence interval from sample data. Let a be the level of signifi cance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean.

(A corresponding relationship between confi dence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, m1  m2, and p1  p2, which we will study in Sections 9.3, 10.2, and 10.3.) Whenever the value of k given in the null hypothesis falls outside the c 5 1  a confi dence interval for the parameter, we reject H0. For example, consider a two-tailed hypothesis test with a 5 0.01 and H0: m 5 20 H1: m ? 20 A random sample of size 36 has a sample mean x 5 22 from a population with standard deviation s 5 4.

(a) What is the value of c 5 1  a? Using the methods of Chapter 8, construct a 1  a confi dence interval for m from the sample data. What is the value of m given in the null hypothesis (i.e., what is k)? Is this value in the confi dence interval? Do we reject or fail to reject H0 based on this information?

(b) Using methods of this chapter, fi nd the P-value for the hypothesis test.
Do we reject or fail to reject H0? Compare your result to that of part (a).