Question 1076795: Could someone help me with the lower and upper, I have everything else and can't seem to get them, thank you!
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 later.) 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 = 0.01 and
H0: μ = 20 H1: μ ≠ 20
A random sample of size 39 has a sample mean x = 23 from a population with standard deviation σ = 6.
(a) What is the value of c = 1 − α?
.99
Correct: Your answer is correct.
Construct a 1 − α confidence interval for μ from the sample data. (Round your answers to two decimal places.)
lower limit
upper limit
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If it is a two-tailed test with a 99% confidence interval, we want z=0.995
interval width is +/- 2.576*6/sqrt(39)=2.47
The interval is 23+/- 2.47 or (20.53, 25.47)
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