MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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 ? be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the
For a two-tailed hypothesis test with level of significance ? 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 ? = 0.01 and
H0: μ = 21
H1: μ ≠ 21
H1: μ ≠ 21
A random sample of size 20 has a sample mean x = 19 from a population with standard deviation σ = 7.
(b) Using methods of Chapter 8, find the P-value for the hypothesis test. (Round your answer to four decimal places.)
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