Hypothesis Testing and Errors

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, calculating the rejection region, and expressing it in terms of the sample mean. The tutorial also discusses type I and type II errors, including how to calculate the probability of a type II error and the power of a test. It concludes with power calculations under different alternative hypotheses.

What is the main focus of the video tutorial?

• Calculating the mean of a sample

• Understanding power and type II error in hypothesis testing

• Learning about standard deviation

• Exploring different types of distributions

In the context of the video, what is the known parameter of the population?

• Population mean

• Sample mean

• Population standard deviation

• Sample standard deviation

What is the significance level used in the hypothesis test?

• 0.10

• 0.09

• 0.01

• 0.05

For what values of Z will the null hypothesis be rejected?

• Z = 0

• Z < -1.34

• Z > 0

• Z > 1.34

How is the rejection region reexpressed in terms of the sample mean?

• X bar > 50

• X bar >= 45.31

• X bar < 50

• X bar <= 45.31

What does the shaded area in the visualization represent?

• Probability of a type I error

• Probability of a type III error

• Probability of a type II error

• Probability of a correct decision

What is the probability of committing a type II error when the true mean is 43?

• 0.745

• 0.255

• 0.09

• 0.5

How is the probability of a type II error calculated?

• By finding the area under the entire curve

• By finding the area to the right of the Z value

• By finding the area to the left of the Z value

• By finding the area between two Z values

What is the power of a test?

• Probability of accepting the null hypothesis when it is true

• Probability of committing a type II error

• Probability of committing a type I error

• Probability of rejecting the null hypothesis when it is false

In the example where the true mean is 40, what is the power of the test?

• 0.935

• 0.255

• 0.745

• 0.5