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