Midterm 2

Question 1

True or False?

It is possible that the type II error probability is very small, but the probability of H₀ being true is large.

Answer 1

True

Question 2

True or False?

If the null hypothesis and alternative hypothesis are both simple, then a most powerful critical region of size a = .05 exists and can be created using Neyman-Pearson Lemma.

Answer 2

False

Question 3

True or False?

A p-value indicates how extreme the observed sample is when H₀ is true.

Answer 3

True

Question 4

True or False?

If the null hypothesis and alternative hypothesis are both simple, then the critical region of the Likelihood Ratio Test is the same as the critical region obtained via Neyman-Pearson Lemma.

Answer 4

False

Question 5

True or False?

A larger p-value implies more likely the null hypothesis being true.

Answer 5

False

Question 6

What is the probability of a type I error a?

Answer 6

The probability that we reject the null hypothesis when it is true

Question 7

What is the probability of a type II error B?

Answer 7

The probability that we accept the null hypothesis when it is false