Is there a relationship between confidence intervals andtwo-tailed hypothesis tests? Let c be the level ofconfidence used to construct a confidence interval from sampledata. Let α be the level of significance for a two-tailedhypothesis test. The following statement applies to hypothesistests of the mean.

For a two-tailed hypothesis test with level of significanceα and null hypothesis H₀: μ =k, we reject H₀ wheneverk falls outside the c = 1–  α confidence interval for μbased onthe sample data. When k falls within the c = 1–  α confidence interval, we do not rejectH₀.

(A corresponding relationship between confidence intervals andtwo-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 fallsoutside the c = 1 –  αconfidence interval for the parameter, we rejectH₀. For example, consider a two-tailed hypothesistest with α = 0.05and

H₀: μ = 21
H₁: μ ≠ 21

A random sample of size 33 has a sample mean x = 22from a population with standard deviation σ = 3.

(a) What is the value of c = 1 − α?


Using the methods of Chapter 7, construct a 1 − αconfidence interval for μ from the sample data. (Roundyour answers to two decimal places.)

lower limit   Â
upper limit   Â

What is the value of μ given in the null hypothesis (i.e.,what is k)?
k =