Relationship between confidence intervals and hypothesis tests

14 Relationship between confidence intervals and hypothesis tests 

Confidence intervals can be used to test a number of hypotheses. This is illustrated using the study data from the previous example in Section 6.12. 

Scientists from the pharmaceutical company believe that reporting a 95% confidence interval for the population mean change in SBP may prove helpful. Following the confidence interval defined in Section 6.10, a 95% confidence interval for the population mean is  

The scientists can report from this study that they are 95% confident that the true population mean change in SBP is within the interval (-12.1, -1.9). One interpretation of this interval is that the scientists are 95% confident that the drug works by reducing SBP, as evidenced by an upper limit of the confidence interval that is less than 0. Another less favorable interpretation is that the drug does not work all that well - after all, the confidence interval does not rule out some very minor reductions in SBP (upper limit of -1.9 mmHg). It is true that, had the scientists hypothesized a value of the population mean outside of the values of this 95% confidence interval, the null hypothesis would have been rejected at the a = 0.05 level. For example, the following null hypotheses would have been rejected  

Conversely, the following null hypotheses would not have been rejected  

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