The power of a significance test for a particular value of the parameter is computed to be 0.93. Which statement below is true?
a) The probability of committing a Type I error is 0.07.
b) The probability of committing a Type I error is 0.93.
c) The probability of committing a Type II error is 0.07.
d) The probability of committing a Type II error is 0.93.
e) The probability of committing a Type II error is the same as the alpha level.
To determine which statement is true, we need to understand the concept of Type I and Type II errors in hypothesis testing.
Type I error occurs when we reject a null hypothesis that is actually true. This error is also known as a "false positive". It is typically denoted by the symbol α (alpha) and represents the significance level or the probability of rejecting a true null hypothesis.
Type II error occurs when we fail to reject a null hypothesis that is actually false. This error is also known as a "false negative". It is typically denoted by the symbol β (beta) and represents the probability of failing to detect a false null hypothesis.
Now, let's analyze the options given:
a) The probability of committing a Type I error is 0.07.
b) The probability of committing a Type I error is 0.93.
c) The probability of committing a Type II error is 0.07.
d) The probability of committing a Type II error is 0.93.
e) The probability of committing a Type II error is the same as the alpha level.
Based on the given information that the power of the significance test is 0.93, we can conclude that option d) is true. The information provided does not directly mention the alpha level, so we cannot determine the exact value of α or the probability of committing a Type I error.