Hypothesis Testing Concepts and Errors

The video tutorial explains the concepts of power and Type II error in hypothesis testing, focusing on a two-tailed Z test for a single mean. It covers the setup of the hypothesis test, calculation of rejection regions, and the determination of power and Type II error probabilities. The tutorial uses examples to illustrate how power increases as the true mean deviates from the hypothesized mean.

What is the focus of the example discussed in the video?

• A one-tailed F test

• A one-tailed t-test

• A chi-square test

• A two-tailed Z test

What is a Type I error in hypothesis testing?

• Accepting the null hypothesis when it is false

• Rejecting the null hypothesis when it is true

• Accepting the alternative hypothesis when it is false

• Rejecting the alternative hypothesis when it is true

What does the significance level alpha represent?

• The probability of a Type II error

• The probability of a Type I error

• The power of the test

• The sample size

In the hypothesis test setup, what is known about the population?

• The sample size is unknown

• The population mean is known

• The population standard deviation is known

• The population standard deviation is unknown

What is the significance level chosen for the hypothesis test?

• 0.01

• 0.05

• 0.10

• 0.20

What are the Z values that define the rejection region for a two-tailed test?

• -1.64 and 1.64

• -1.96 and 1.96

• -2.58 and 2.58

• -1.28 and 1.28

For what sample mean values will the null hypothesis be rejected?

• Less than or equal to 70.00 or greater than or equal to 80.00

• Less than or equal to 71.08 or greater than or equal to 78.92

• Less than or equal to 72.00 or greater than or equal to 77.00

• Less than or equal to 73.00 or greater than or equal to 76.00

What is the power of the test if the true mean is 76?

• 0.921

• 0.079

• 0.830

• 0.170

How is the probability of a Type II error calculated?

• The difference between alpha and beta

• 1 minus the significance level

• The sum of the power and alpha

• 1 minus the power of the test

What is the probability of a Type II error if the true mean is 77?

• 0.170

• 0.921

• 0.079

• 0.830