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Hypothesis Testing With a 95% Confidence Interval for Mean

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We have created 95% confidence interval for mean; with the result (10, 15). What decision will we make if we test H0 : mean = 16 versus H1 : mean is not equal to16 at alpha = 0.025?

Reject H0 in favor of H1.
Accept H0 in favor of H1.
Fail to reject H0 in favor of H1.
We cannot tell what our decision will be from the information given.

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Solution Summary

This solution first explains the steps in calculating sample mean and standard error from the given confidence intervals. Then it tests for mean at different confidence level.

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Let estimated mean is X and standard error is Y.

Lower bound for interval estimate = X-Z*standard error =X-Z*Y =10
Upper bound for interval estimate = X+Z*standard error=X+Z*Y=15

Z at 95% confidence level is 1.96
So, we get following ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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