Asked by Holly Phillip on Jun 10, 2024
Verified
If the probability of committing a Type I error for a given test is to be decreased, then for a fixed sample size n, which of the following statements is true?
A) The power of the test will increase.
B) The probability of committing a Type II error will increase.
C) The probability of committing a Type II error will decrease.
D) A two-tailed test must be used.
E) The probability of committing a Type II error will decrease and a two-tailed test must be used.
Type I Error
The flawed dismissal of an actual null hypothesis, popularly identified as a "false positive."
Power Of The Test
The probability that a statistical test will correctly reject a false null hypothesis, essentially measuring the test's ability to detect an effect if there is one.
- Pinpoint Type I and Type II errors during hypothesis testing and detail their effects.
- Comprehend how the size of a sample influences the likelihood of error occurrence in hypothesis testing.
- Understand the relationship between the level of significance, power of the test, and the probabilities of committing Type I and Type II errors.
Verified Answer
LS
Laryssa SantiagoJun 15, 2024
Final Answer :
B
Explanation :
Decreasing the probability of committing a Type I error (rejecting a true null hypothesis) generally involves making the criteria for rejecting the null hypothesis more stringent. This, in turn, makes it harder to detect a true effect when there is one, thus increasing the probability of committing a Type II error (failing to reject a false null hypothesis).
Learning Objectives
- Pinpoint Type I and Type II errors during hypothesis testing and detail their effects.
- Comprehend how the size of a sample influences the likelihood of error occurrence in hypothesis testing.
- Understand the relationship between the level of significance, power of the test, and the probabilities of committing Type I and Type II errors.
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