Which of the following regarding the Type I and Type II errors of a significance test is/are correct? Select all that apply. a. The power of test = 1 - P(Type II error) b. P(Type II error) = 1 - P(Type I error) c. For a fixed significance level α, the probability of a Type I error increase when the sample size increases. d. For a fixed significance level α, the probability of a Type II error increases when the sample size increases. e. The probability of a Type II error would decrease if the true population parameter value is further away from the presumed parameter value stated in the null hypothesis. f. For a fixed sample size n, the probability of a Type II error increases when the probability of a Type I error decreases.

The sentences that are correct regarding Type I and Type II errors of a significance test:

a. The power of test = 1 - P(Type II error)

c. For a fixed significance level α, the probability of a Type I error increase when the sample size increases.

e. The probability of a Type II error would decrease if the true population parameter value is further away from the presumed parameter value stated in the null hypothesis.

f. For a fixed sample size n, the probability of a Type II error increases when the probability of a Type I error decreases.

Step-by-step explanation:

We can analyse point by point as follows:

a. The power of test = 1 - P(Type II error). This is true, the power of a test is defined as

P = 1 - β, where P is the power of the test and β is the probability to commit Type II error.

b. P(Type II error) = 1 - P(Type I error). This is false, the probability of commit a Type II error is β and is related with the power of the test by P = 1 - β. The probability to commit Type I error is defined by α (the significance level) and the relationship between these two parameter is: α≤β.

c. For a fixed significance level α, the probability of a Type I error increase when the sample size increases. This is true, for a fixed significance level when population size increases, the power of the test increase too. That means the probability to commit type II (β) error diminishes and as well as there is an inverse relationship between α y β, the first one would be higher.

d. For a fixed significance level α, the probability of a Type II error increases when the sample size increases. This is false, when the sample size increases, the probability to commit a Type II error diminish and as a consequence, the power of the test increases (because of the relationship between these values showed in point a.)

e. The probability of a Type II error would decrease if the true population parameter value is further away from the presumed parameter value stated in the null hypothesis. This is true population parameter value is further away from the presumed value stated in H0, the chances to do not reject H0 when it is actually (Type II error) false will be lower.

f. For a fixed sample size n, the probability of a Type II error increases when the probability of a Type I error decreases. This is true, these two error are inversely related so, when the probability to commit a Type I error (α) diminishes, β (probability to commit Type II error) increases.

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step-by-step explanation:

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