SOLUTION: I have several questions to this nature...I need an easy explanation as to how these are figured. This one has an answer of "C". Assume that in a hypothesis test with null hypo

Question 319852: I have several questions to this nature...I need an easy explanation as to how these are figured. This one has an answer of "C".
Assume that in a hypothesis test with null hypothesis μ 0 H : = 16.0 at α = 0.10, that a value of 14.0 for the sample mean results in the null hypothesis being accepted. That corresponds to a confidence interval result of
A) There is insufficient information to conclude whether the 95% confidence interval
for the mean contains or does not contain the value 16.0
B) The 95% confidence interval for the mean contains the value 14.0
C) The 95% confidence interval for the mean contains the value 16.0
D) The 95% confidence interval for the mean does not contain the value 16.0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I have several questions of this nature...I need an easy explanation as to how these are figured. This one has an answer of "C".
-------------------------
Assume that in a hypothesis test with null hypothesis
Ho: u = 16
α = 0.10
----
If this is a two-tail test, each tail contains 5% of the population
and the 90% acceptance interval is centered on u = 16.
------
If a value of 14.0 for the sample mean results in the null hypothesis being accepted.
--
So x=14 is not in the rejection interval.
------------------------

That corresponds to a confidence interval result of
A) There is insufficient information to conclude whether the 95% confidence interval for the mean contains or does not contain the value 16.0
------
B) The 95% confidence interval for the mean contains the value 14.0
------
C) The 95% confidence interval for the mean contains the value 16.0
Yes. The confidence interval confirms Ho, that the mean is 16.
------
D) The 95% confidence interval for the mean does not contain the value 16.0
--------------------------
Cheers,
Stan H.

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