8. True or False: When using data from the same sample, the 95% confidence interval for...

8. True or False: When using data from the same sample, the 95% confidence interval for µ will always support the results from a 2-sided, 1 sample t-test. Explain your reasoning.

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Solution:

Statement: When using data from the same sample, the 95% confidence interval for µ will always support the results from a 2-sided, 1 sample t-test

True.

Confidence interval gives the interval estimate for parameter of population.

95% confidence interval for µ gives two limits, in which population parameter fall with 95% confidence.

Results in hypothesis testing is same as results obtained from confidence interval.

In hypothesis testing , we reject null hypothesis, if value of the test statistic below left tail critical value or above the right tail critical value, otherwise we fail to reject H0.

Similarly in case of confidence interval, we reject H0, if population parameter µ is less than lower limit of confidence interval or above the upper limit confidence interval.

Thus the 95% confidence interval for µ will always support the results from a 2-sided, 1 sample t-test , otherwise we fail to reject H0.

orchestra answered 1 year ago

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