Assume that a researcher wants to use sample data to test the claim that the sam

Question

Assume that a researcher wants to use sample data to test the claim that the sample is from a population with a standard deviation less than 1.8 min. The researcher will use a 0.05 significance level to test that claim. If the researcher wants to use the confidence interval method of testing hypotheses, what level of confidence should be used for the confidence interval? Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the P-value method or the critical value method?

Explanation / Answer

if the researcher uses the confidence interval method of testing hypotheses then the rejection region is both sided not one sided.

so to keep same significance level 0.05 to test that claim ,the confidence that he should use is 0.05 but the standard error in the interval should be based upon the confidence 0.05/2=0.025 since the rejection region is both sided not one sided.

yes. the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the P-value method or the critical value method.

because if the test is accepted by P value method or critical value method then obviously the confidence interval will contain the value 1.8

and if it is rejected then the point 1.8 will lie outside the confidence interval.

hence both the conclusions will be same [answer]

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