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Errors in medical tests. Medical tests have been developed
Chapter 7, Problem 127SE(choose chapter or problem)
Errors in medical tests. Medical tests have been developed to detect many serious diseases. A medical test is designed to minimize the probability that it will produce a “false positive” or a “false negative.” A false positive refers to a positive test result for an individual who does not have the disease, whereas a false negative is a negative test result for an individual who does have the disease.
a. If we treat a medical test for a disease as a statistical test of hypothesis, what are the null and alternative hypotheses for the medical test?
b. What are the Type I and Type II errors for the test? Relate each to false positives and false negatives.
c. Which of the errors has graver consequences? Considering this error, is it more important to minimize \(\alpha\) or \(\beta\) Explain.
Questions & Answers
QUESTION:
Errors in medical tests. Medical tests have been developed to detect many serious diseases. A medical test is designed to minimize the probability that it will produce a “false positive” or a “false negative.” A false positive refers to a positive test result for an individual who does not have the disease, whereas a false negative is a negative test result for an individual who does have the disease.
a. If we treat a medical test for a disease as a statistical test of hypothesis, what are the null and alternative hypotheses for the medical test?
b. What are the Type I and Type II errors for the test? Relate each to false positives and false negatives.
c. Which of the errors has graver consequences? Considering this error, is it more important to minimize \(\alpha\) or \(\beta\) Explain.
ANSWER:Solution
Step 1 of 3
a) We have to write null and alternative hypothesis for the test
The null hypothesis The individual don’t have the disease
The alternative hypothesis The individual have the disease