Question

Two types of incorrect decisions can be made in a hypothesis test. a type I error and type II error.

a. Explain the meaning of each type of error.

b. Identify the letter used to represent the probability of each type of error.

c. If the null hypothesis is in fact true, only one type of error is possible. Which type is that? Explain your answer.

d. If you fail to reject the null hypothesis, on ly one type of error is possible. Which type is that? Explain your answer.

Short answer

a).

A type-I error occur when we reject a null hypothesis which is in fact true.

A type-II error occur when we do not reject a null hypothesis which is in fact false.

b).

Probability of type-I error is represented by$\alpha$

Probability of type-II error is represented by $\beta$.

c). Type-I error

d). Type-II error

Step-by-step solution

Step 1. (a). Meaning

A type-I error occur when we reject a null hypothesis which is in fact true.

A type-II error occur when we do not reject a null hypothesis which is in fact false.

Step 2. (b). Letters to represent population

Probability of type-I error is represented by $\alpha$

Probability of type-II error is represented by $\beta$.

Step 3. (c). Explanation

Type-I error

if the null hypothesis is in fact true then the only possible incorrect decision or error is rejecting the null hypothesis.

Step 4. (d). Explanation

Type-II error

If we fail to reject the null hypothesis then the only possible incorrect decision or error occurs if the null hypothesis is in fact false.