Question 1078507: nEED HELP WITH LOWER, UPPER AND P VALUE
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 = 5.
(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
17.57
Incorrect: Your answer is incorrect.
upper limit
25.17
Incorrect: Your answer is incorrect.
What is the value of μ given in the null hypothesis (i.e., what is k)?
k =
20
Correct: Your answer is correct.
Is this value in the confidence interval?
Yes
No
Correct: Your answer is correct.
Do we reject or fail to reject H0 based on this information?
We fail to reject the null hypothesis since μ = 20 is not contained in this interval.
We fail to reject the null hypothesis since μ = 20 is contained in this interval.
We reject the null hypothesis since μ = 20 is not contained in this interval.
We reject the null hypothesis since μ = 20 is contained in this interval.
Correct: Your answer is correct.
(b) Using methods of this chapter, find the P-value for the hypothesis test. (Round your answer to four decimal places.)
.0034
Incorrect: Your answer is incorrect.
thANK YOU!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The 99% CI is mean +/- z(0.995) sigma/sqrt(39)
(20.94, 25.06)
This is 2.576*5/sqrt(39)=2.06
20 is not in the CI
p-value will be very small.
It is <0.0002
Note: if the CI doesn't contain what is hypothesized, the p-value is less than alpha.
If the p-value is less than alpha, the CI won't contain the CI. That is a basic check to do.
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