객관식
Which of the following is not a criterion for making a decision in a hypothesis test?
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
객관식
Which of the following is not a true statement about error in hypothesis testing?
A
A Type I error occurs when the null hypothesis is rejected when it is actually true.
B
Reducing the probability of a Type I error may increase the probability of a Type II error.
C
A Type II error occurs when the null hypothesis is not rejected when it is actually false.
D
The probability of a Type I error is denoted by .
검증된 단계별 안내1
Step 1: Understand the definitions of Type I and Type II errors in hypothesis testing. A Type I error occurs when the null hypothesis (H0) is rejected even though it is true, and a Type II error occurs when the null hypothesis is not rejected even though it is false.
Step 2: Recognize the notation used for the probabilities of these errors. The probability of a Type I error is denoted by \(\alpha\), and the probability of a Type II error is denoted by \(\beta\).
Step 3: Analyze each statement given in the problem: The first statement correctly describes a Type I error. The second statement correctly explains the trade-off between Type I and Type II errors. The third statement correctly describes a Type II error.
Step 4: Identify the incorrect statement by focusing on the notation: The statement that says "The probability of a Type I error is denoted by \(\beta\)" is false because \(\beta\) represents the probability of a Type II error, not Type I.
Step 5: Conclude that the incorrect statement is the one mislabeling the probability of a Type I error as \(\beta\) instead of \(\alpha\).
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