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 μbased 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 14 has a sample mean x = 19 from a population with standard deviation σ = 5.
(a) What is the value of c = 1 − α?
Using the methods of Chapter 7, construct a 1 − α confidence interval for μ from the sample data. (Round your answers to two decimal places.)
Lower Limit: 16.38
Upper Limit: 21.62
What is the value of μ given in the null hypothesis (i.e., what is k)?
k = 21
Is this value in the confidence interval?
Do we reject or fail to reject H0 based on this information?
Fail to reject, since μ = 21 is contained in this
(b) Using methods of Chapter 8, find the P-value for the hypothesis test. (Round your answer to four decimal places.)
Get Answers For Free
Most questions answered within 1 hours.