A certain experimental drug claims a cure rate of at least 75% for males with prostate cancer. Describe both the
Type I and Type II errors in context.
State the null and alternative hypothesis.
H0:
Ha:
Type I error, the null hypothesis is true (in context):
Type II error, the null hypothesis is false (in context):
Which error is the more serious?
Solution:
The null and alternative hypotheses for the given test scenario is given as below:
Null hypothesis: H0: A cure rate for males with prostate cancer is at least 75%.
Alternative hypothesis: Ha: A cure rate for males with prostate cancer is less than 75%.
Type I error: For this test, the type I error occurred when we conclude that a cure rate for males with prostate cancer is less than 75%, however, in fact, the cure rate is at least 75% actually.
Type II error: For this test, the type II error occurred when we conclude that a cure rate for males with prostate cancer is at least 75%, however, in fact, the cure rate is less than 75% actually.
Type II error is the more serious.
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