EXAMPLE 5 Statistical significance

Suppose that you are a researcher for a pharmaceutical research company. You are investigating the side effects of a new cholesterol-lowering medication and want to determine whether the medication will decrease the population mean systolic blood pressure level from the current population mean of . If so, then a warning will have to be given not to prescribe the new medication to patients whose blood pressure is already low.

To determine which of these hypotheses is correct, we take a sample of randomly selected patients who are taking the medication. We record their systolic blood pressure levels and calculate the sample mean and sample standard deviation s. Most likely, the mean of this sample of patients' systolic blood pressure levels will not be exactly equal to 110, even if the null hypothesis is true. Now, suppose that the sample mean blood pressure is less than the hypothesized population mean of 110. Is the difference due simply to chance variation, or is it evidence of a real side effect of the cholesterol medication?

  1. Construct the appropriate hypotheses.
  2. For and , discuss whether each result would be statistically significant or due to chance.

Solution

  1. The key word “decrease” means we have a left-tailed test. “Less than what?” The current population mean systolic blood pressure of . Thus, our hypotheses are:

    where represents the population mean systolic blood pressure and .

    493

  2. For , the difference between and is only 1. Depending on the variability present in the sample, the researcher would likely not reject the null hypothesis because this small difference is probably due to chance variation. The result is probably not statistically significant. But, for , the difference between and is 20. Depending on the variability present in the sample, the researcher would probably conclude that this difference is so large that it is unlikely that it is due to chance variation. Thus, the researcher would probably reject the null hypothesis in favor of the alternative hypothesis . The result is statistically significant.

Note: When we reject , we say that the results are statistically significant. If we do not reject , the results are not statistically significant.