AP Statistics Question 236: Answer and Explanation

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Question: 236

6. Which of the following is a true statement about hypothesis testing?

• A. If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.
• B. Whether to use a one- or a two-sided test is typically decided after the data are gathered.
• C. If a hypothesis test is conducted at the 1% level, there is a 1% chance of rejecting the null hypothesis.
• D. The probability of a Type I error plus the probability of a Type II error always equal 1.
• E. The power of a test concerns its ability to detect an alternative hypothesis.

Correct Answer: E

Explanation:

(E) If the P -value is less than 0.10, it does not follow that it is less than 0.05. Decisions such as whether a test should be one- or two-sided are made before the data are gathered. If α = 0.01, there is a 1% chance of rejecting the null hypothesis if the null hypothesis is true. There is one probability of a Type I error, the significance level, while there is a different probability of a Type II error associated with each possible correct alternative, so the sum does not equal 1.

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