Hypothesis Testing -- Duality with Confidence Intervals

It is not necessary to understand this method for Test 3.

You will need it later -- in the chapters on comparing two paramters. You can postpone this until later if you wish.

Example 1:

Suppose I form and interpret a 95% confidence interval: "I have 95% confidence that the population mean is between 121 and 131."

Then suppose, for the same data, I want to test these hypotheses at the 5% significance level. (You should write these with symbols. I'm just avoiding having to use a fancy format for this web page.)
null hypothesis: pop'n mean = 127
alternative hypothesis: pop'n mean not equal to 127

Since the 127 is in the confidence interval, then the null hypothesis is consistent with the confidence interval. So I cannot reject the null hypothesis.

Example 2:

Suppose I form and interpret a 95% confidence interval: "I have 95% confidence that the population mean is between 116 and 126."

Then suppose, for the same data, I want to test these hypotheses at the 5% significance level:
null hypothesis: pop'n mean = 127
alternative hypothesis: pop'n mean not equal to 127

Since the 127 is not in the confidence interval, then the null hypothesis is not consistent with the confidence interval. So I must reject the null hypothesis.

Last updated October 22, 2006 . Mary Parker