Errors and Power Practice

In a type 1 error...

• the null is true but we reject it

• the null is true and we fail to reject it

• the null is false and we reject it

• the null is false but we fail to reject it

In a Type 2 error...

• the null is true but we reject it

• the null is true and we fail to reject it

• the null is false and we reject it

• the null is false but we fail to reject it

Power is the probability that...

• we reject the null when it is false

• we fail to reject the null when it is false

• we reject the null when it is true

• we fail to reject the null when it is true

Tags

CCSS.HSS.MD.A.2

An experiment is conducted to determine whether a new treatment helps patients with diabetes.

H0: The treatment does not work.

Ha: The treatment works.

Which of the following is a Type I Error in this situation?

• the treatment does not work, but we believe that it does

• the treatment does not work, and we believe it does not work

• the treatment works, and we believe that it works

• the treatment works, but we think that it doesn't

Tags

CCSS.HSS.IC.B.3

An experiment is conducted to determine whether a new treatment helps patients with diabetes.

H0: The treatment does not work.

Ha: The treatment works.

Which of the following is a Type II Error in this situation?

• the treatment does not work, but we believe that it does

• the treatment does not work, and we believe it does not work

• the treatment works, and we believe that it works

• the treatment works, but we think that it doesn't

An experiment is conducted to determine whether a new treatment helps patients with diabetes.

H0: The treatment does not work.

Ha: The treatment works.

Which of the following would NOT be errors in this situation? (select all that apply)

• the treatment does not work, but we believe that it does

• the treatment does not work, and we believe it does not work

• the treatment works, and we believe that it works

• the treatment works, but we think that it doesn't

A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested is higher than 40%, in which case they would consider building the new cafeteria. Here are the hypotheses they'll use:

H0: p = 0.40,  Ha: p > 0.40

In a Type (a)   error, the university will build a new cafeteria when the students don't want it. 

Tags

CCSS.HSS.IC.B.3

A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested is higher than 40%, in which case they would consider building the new cafeteria. Here are the hypotheses they'll use:

H0: p = 0.40, Ha: p > 0.40

In a Type (a)   error, the university will not build a new cafeteria when the students want it.

What can you do to lower the probability of making a Type I error? (check all that apply)

• Choose a smaller alpha

• Choose a larger alpha

• Choose a larger sample

• Choose a smaller sample

What can you do to lower the chance of making a Type II Error? (check all that apply)

• choose a smaller alpha

• choose a larger alpha

• choose a larger sample size

• choose a smaller sample size

Tags

CCSS.HSS.MD.A.2