Power and Errors in Hypothesis Testing

The video tutorial explains the concepts of power and type II error in hypothesis testing, focusing on a one-sample Z test. It covers setting up the hypothesis test, determining the rejection region, and expressing it in terms of the sample mean. The tutorial also discusses type I and type II errors, calculating the probability of a type II error, and understanding the power of a test. It concludes with power calculations under different alternative hypotheses.

What is the significance level used in the hypothesis test example?

• 0.09

• 0.05

• 0.01

• 0.10

In the context of the Z test, what does the rejection region represent?

• Values of Z where the alternative hypothesis is accepted

• Values of Z where the test is inconclusive

• Values of Z where the null hypothesis is rejected

• Values of Z where the null hypothesis is accepted

What is the probability of committing a type I error in this test?

• 0.5

• 0.745

• 0.255

• 0.09

What is a type II error in hypothesis testing?

• Accepting the alternative hypothesis when it is false

• Rejecting the null hypothesis when it is true

• Accepting the null hypothesis when it is false

• Rejecting the alternative hypothesis when it is true

How is the probability of a type II error calculated when the true mean is 43?

• By finding the area between the true mean and the hypothesized mean

• By finding the area to the right of the rejection region

• By finding the area under the entire normal curve

• By finding the area to the left of the rejection region

What is the value of beta, the probability of a type II error, when the true mean is 43?

• 0.5

• 0.09

• 0.255

• 0.745

What is the power of the test when the true mean is 43?

• 0.255

• 0.745

• 0.09

• 0.5

When the true mean is 40, what is the power of the test?

• 0.255

• 0.09

• 0.935

• 0.5

What does the power of a test represent?

• Probability of rejecting the alternative hypothesis when it is true

• Probability of accepting the alternative hypothesis when it is false

• Probability of rejecting the null hypothesis when it is false

• Probability of accepting the null hypothesis when it is true

How does the power calculation change for different alternative hypotheses?

• Neither the logic nor the required areas change

• The logic changes, but the required areas remain the same

• The logic and required areas remain the same

• The logic remains the same, but the required areas change