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".
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Assume that in a hypothesis test with null hypothesis
Ho: u = 16
α = 0.10
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If this is a two-tail test, each tail contains 5% of the population
and the 90% acceptance interval is centered on u = 16.
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If a value of 14.0 for the sample mean results in the null hypothesis being accepted.
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So x=14 is not in the rejection interval.
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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
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B) The 95% confidence interval for the mean contains the value 14.0
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C) The 95% confidence interval for the mean contains the value 16.0
Yes. The confidence interval confirms Ho, that the mean is 16.
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D) The 95% confidence interval for the mean does not contain the value 16.0
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Cheers,
Stan H.
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