Question

Which of the following statements is FALSE?

• a.) The power of a hypothesis test is the probability of not making a Type II error.
• b.) Alpha (α) is equal to the probability of making a Type I error.
• c.) The probability of rejecting the null hypothesis when the null hypothesis is true is called a Type I Error.
• d.) A smaller sample size would increase the effectiveness of a hypothesis test.

Answer 1

Answer:

Given that,

(a).

The power of a hypothesis test is the probability of not making a Type Il error:

$\rightarrow$ The power is 1- the probability of type two error. That means the power of the hypothesis test is not making type two error.

True.

(b).

Alpha (α) is equal to the probability of making a Type I error:

$\rightarrow$ The actual value of the probability of type one error for the test under consideration is known as the size of the test, the value of supremum of the probability of type one error is the size. But the probability of type one error is the significance level.

So true.

(c).

The probability of rejecting the null hypothesis when the null hypothesis is true is called a Type I Error:

$\rightarrow$ Type one error is the probability of rejecting the Null hypothesis H0 when the null hypothesis is true.

So true.

(d).

A smaller sample size would increase the effectiveness of a hypothesis test:

$\rightarrow$ As the sample size increases, the power of the test also increases.so the effectiveness of the test increases. So a smaller sample size would not increase the effectiveness of the test.

False.

Therefore,

So the false Statement is d.