EXAMPLE 6 Type I and Type II errors

For the medication hypothesis test in Example 5, explain what it would mean if the following errors were made:

  1. Type I error
  2. Type II error

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Solution

The hypotheses in Example 5 were the following:

where represents the population mean systolic blood pressure.

  1. A Type I error occurs when we reject when is true. This would be to conclude that had decreased when, in reality, it had stayed the same. In other words, a Type I error would be to conclude that the population mean systolic blood pressure had decreased when, in reality, it had not decreased. The pharmaceutical company, afraid of this possible side effect, might not continue production of the drug when, in reality, there is no side effect.
  2. A Type II error occurs when we do not reject when is false. This would be to conclude that had stayed the same when, in reality, it had decreased. In this case, this is a very dangerous error to make, because the pharmaceutical company might then conclude that the side effect does not exist when, in reality, it does exist, and it could lead to dangerous lowering of blood pressure. This is why the Food and Drug Administration requires that strict protocols are followed regarding Type I and Type II errors when approving new medications for the market.

NOW YOU CAN DO

Exercises 19–22.