Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let e be the level of confidence used to construct a confidence

Burhan Hopper

Burhan Hopper

Answered question

2021-06-01

Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let e 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. (A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters such as p, mu1μ2, or p1p2, which we will study in Section 9.3, 10.2, and 10.3.) Whenever the value of k given in the null hypothesis falls outside the c=1α confidence interval for the parameter, we reject H0. For example, consider a two-tailed hypothesis test with α=0.01 and H0:μ=20H1:μ20 sample mean x¯=22 from a population with standard deviation σ=4.
(a) What is the value of cc=1α;. Using the methods, construct a c=1α; confidence interval for μ from the sample data. What is the value of μ; given in the null hypothesis (i.e., what is k)? Is this value in the confidence interval? Do we reject or fail to reject H0 based on this information?
(b) using methods, find the P-value for the hypothesis test. Do we reject or fail to reject H0? Compare your result to that of part (a).

Answer & Explanation

liannemdh

liannemdh

Skilled2021-06-02Added 106 answers

(a)c=0.99=99%
20.2833 to 23.7167
μ=20 is not in the confidence interval
Reject the null hypothesis H0.
(b)Reject H0
Same conclusion as in part (a)

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