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 α 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 α and null hypothesis h0: μ = k, we reject h0 whenever k falls outside the c = 1 – α confidence interval for μ based on the sample data. when k falls within the c = 1 – α confidence interval, we do not reject h0. (a corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, μ1 − μ2, 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 – α confidence interval for the parameter, we reject h0. for example, consider a two-tailed hypothesis test with α = 0.05 and h0: μ = 21 h1: μ ≠ 21 a random sample of size 29 has a sample mean x = 20 from a population with standard deviation σ = 8. (a) what is the value of c = 1 − α?