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Question about Type I and Type II Error

Read the passage below, and then consider the following scenario.

A physician is trying to decide whether to prescribe medication for cholesterol reduction in a 45-year-old female patient. The null hypothesis is that the patient's cholesterol is less than the threshold of treatable hypercholesterolemia. However, a sample of readings over a 2-year time period shows considerable variation, usually below but sometimes above the threshold.

(a) Define Type I and Type II error.
(b) List the costs of each type of error (in general terms). Who bears the cost of each?
(c) How might the patient's point of view differ from the HMO's or doctor's?
(d) In what sense is this a business problem? A societal problem? An individual problem?

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Hypercholesterolemia is a known risk factor for coronary artery disease. The risk of death from coronary artery disease has a continuous and graded relation to total serum cholesterol levels higher than 180 mg/dl. However, the ratio of total cholesterol to HDL cholesterol is a better predictor of coronary artery disease than the level of either fraction alone. . . . After menopause, plasma LDL cholesterol concentrations rise to equal, and then to exceed, those of men, at the same time HDL cholesterol concentrations fall slightly. . . . This puts women at equal or greater risk for cardiovascular disease. According to the results of medical trials, there is compelling evidence that a reduction in the level of cholesterol leads to a significant decrease in the rate of cardiovascular events. . . . Therefore, screening for high blood cholesterol is an important clinical intervention. The National Heart, Lung, and Blood Institute . . . recommends that all persons aged 20 and above have a cholesterol determination at least once every five years. . . . Timely identification of high-risk individuals allows consideration of various treatment alternatives. For patients who do not have coronary heart disease or peripheral vascular disease, emphasis should be placed on non-pharmacologic approaches, mainly changes in diet and exercise. Drug therapy should be reserved for those at highest risk of coronary heart disease: men above 35 years of age and postmenopausal women. (Source: www.dakotacare.com.)

Solution Preview

Read the passage below, and then consider the following scenario. A physician is trying to decide whether to prescribe medication for cholesterol reduction in a 45-year-old female patient. The null hypothesis is that the patient's cholesterol is less than the threshold of treatable hypercholesterolemia. However, a sample of readings over a 2-year time period shows considerable variation, usually below but sometimes above the threshold.

(a) Define Type I and Type II error.

The null hypothesis is that the patient's cholesterol is low and doesn't need to be treated.
The alternative hypothesis is that her cholesterol is higher than the threshold, and therefore should be treated.

Type I error is a false positive: it happens when you reject the null hypothesis when the null hypothesis is true. This would happen if her cholesterol didn't need to be treated, but it was treated anyway.

Type II error is a false negative: it happens when you fail to reject the null hypothesis when the null hypothesis is false. This would happen if her cholesterol was high and needed to be ...

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