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Hypothesis testing and confidence intervals

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Assume that in a hypothesis test with null hypothesis H 0: mu = 14.0 at alpha = 0.05, that a value of 13.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidence interval result of:

a) the 95% confidence interval for the mean contains the value 14.0
b) the 95% confidence interval for the mean does not contain the value 14.0
c) there is insufficient information as to if the 95% confidence interval for the mean does or does nto contain the value 13.0
d) the 0.05% confidence interval for the mean contains the value 13.0

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Solution Preview

The correct answer is:

b) the 95% confidence interval for the mean does not contain the value 14.0

There is an exact correspondence between confidence intervals and ...

Solution Summary

This solution addresses the correspondence between hypothesis tests and confidence intervals.

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Take a random sample and perform a t-test against a population mean (no time series for any parts of this project.) Test a hypothesis about a population mean. Besides the instructions above, explain what assumptions you made. Note: n must be between 15 to 20! Use no other sample sizes.

Use the same data as 1a and develop a 90% confidence interval and a 95% confidence interval for the population mean. Contrast this to 1a. What additional information or insight did this provide you over the traditional hypothesis testing.

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