Hypothesis Testing Lesson

Multiple Choice

What is the main purpose of hypothesis testing?

• To calculate the mean of the population

• To test claims about population parameters using sample data

• To determine sampling error

• To predict future sample outcomes

Multiple Choice

Why is hypothesis testing important in the field of statistics?

• It helps us test claims and make decisions about populations based on sample data.

• It is only used for collecting data.

• It is not relevant to real-world problems.

• It is used to create new populations.

Multiple Choice

Which of the following is the correct sequence of steps in hypothesis testing?

• Define the population, state the hypothesis, give the significance level, select a sample, collect data, perform calculations, reach a conclusion

• State the hypothesis, define the population, collect data, give the significance level, select a sample, perform calculations, reach a conclusion

• Collect data, define the population, state the hypothesis, select a sample, give the significance level, perform calculations, reach a conclusion

• Give the significance level, define the population, state the hypothesis, select a sample, collect data, perform calculations, reach a conclusion

Multiple Choice

Which of the following is always assumed to be true unless proven otherwise?

• Alternative Hypothesis (H₁)

• Mean Hypothesis (Hμ)

• Null Hypothesis (H₀)

• Critical Hypothesis (Hc)

Multiple Choice

Which of the following statements about hypothesis testing is correct?

• If the sample data supports the hypothesis, we do not reject the hypothesis.

• If the sample data does not support the hypothesis, we accept the hypothesis.

• The hypothesis test is carried out using information obtained by non-random sampling.

• Hypothesis testing does not involve statistical procedures.

Open Ended

Given the scenario: A researcher thinks that if knee surgery patients go to physical therapy twice a week instead of three times, their recovery period will be longer. The average recovery time is 8.2 weeks. What are the null and alternative hypotheses for this test?

Multiple Choice

Which of the following are correct null and alternative hypotheses for testing if college students take less than five years to graduate, on average?

• H0: μ = 5, H1: μ < 5

• H0: μ < 5, H1: μ = 5

• H0: μ > 5, H1: μ < 5

• H0: μ = 5, H1: μ > 5

Open Ended

State the null and alternative hypotheses for the following claim: An engineer claims that the mean number of defects can be increased in a manufacturing process of compact discs by using robots instead of humans for certain tasks. The mean number of defective discs is eleven.

Multiple Choice

Which of the following statements about significance level (α) is correct?

• It is the probability of accepting the null hypothesis when it is false.

• It is the probability of rejecting the null hypothesis when it is true.

• It is always set at 0.10.

• It is unrelated to confidence level.

Multiple Choice

Which of the following pairs of hypotheses and rejection regions is correct for a right-tailed test?

• H0: μ = μ0, H1: μ < μ0; Z < -zα

• H0: μ = μ0, H1: μ > μ0; Z > zα

• H0: μ = μ0, H1: μ ≠ μ0; |Z| > zα/2

• H0: μ = μ0, H1: μ < μ0; Z > zα

Multiple Choice

Which type of hypothesis test is used to detect the difference between the parameters of two populations?

• One-sample test

• Two-sample test

• Paired t-test

• Chi-square test

Multiple Select

Which of the following statements are true about one-tailed hypothesis tests?

• They can be right-tailed or left-tailed.

• They are used when the alternative hypothesis is directional.

• They test for any difference between means.

• They are only used for two-sample tests.

Open Ended

Explain the difference between a one-tailed and a two-tailed hypothesis test.

Multiple Choice

In hypothesis testing, the 'critical region' refers to:

• Where sample data is collected

• Values of the test statistic where we fail to reject the null hypothesis

• Values of the test statistic that lead to rejecting the null hypothesis

• The standard deviation of the sample

Multiple Choice

If the null hypothesis is μ = 30 and the alternative is μ > 30, this is a:

• Two-tailed test

• Left-tailed test

• Right-tailed test

• One-sample test

Open Ended

Describe what happens in a left-tailed one-tailed hypothesis test and how the rejection region is determined.

Multiple Choice

If you are testing whether the mean is not equal to a certain value, which test is appropriate?

• Left-tailed

• Right-tailed

• One-tailed

• Two-tailed

Multiple Choice

The significance level (α) represents:

• The probability of making a Type II error

• The probability of correctly accepting the null hypothesis

• The probability of rejecting a true null hypothesis

• The sample size

Multiple Choice

Which error is also known as a "false negative"?

• Type I error

• Type II error

• Critical error

• Statistical error

Multiple Choice

Match the following errors to their definitions: Type I error and Type II error.

• Type I error: Rejecting H0 when it is true; Type II error: Not rejecting H0 when it is false

• Type I error: Not rejecting H0 when it is false; Type II error: Rejecting H0 when it is true

• Type I error: Accepting H0 when it is true; Type II error: Accepting H0 when it is false

• Type I error: Not rejecting H0 when it is true; Type II error: Rejecting H0 when it is false

Multiple Choice

Which of the following best describes a Type I error in hypothesis testing?

• Rejecting a true null hypothesis

• Failing to reject a true null hypothesis

• Rejecting a false null hypothesis

• Failing to reject a false null hypothesis

Multiple Choice

A Type I error occurs when:

• A false null hypothesis is accepted

• A true null hypothesis is rejected

• A true alternative hypothesis is rejected

• A sample size is too small

Multiple Choice

In the context of hypothesis testing, what does β (beta) represent?

• Probability of a Type I error

• Probability of a Type II error

• Probability of a correct decision

• Probability of rejecting the alternative hypothesis

Multiple Select

Which of the following statements are true about Type II errors?

• It is also called a false negative.

• It occurs when we fail to reject a false null hypothesis.

• It is also called a false positive.

• It is the same as a Type I error.

Multiple Choice

Which step in hypothesis testing involves making a decision to reject or fail to reject the null hypothesis?

• Step 1

• Step 2

• Step 3

• Step 4

Multiple Choice

In a hypothesis test, if Z_test = 2.02 and Z_critical = 1.96 for a right-tailed test, we:

• Fail to reject the null hypothesis

• Accept the null hypothesis

• Reject the null hypothesis

• Cannot determine

Open Ended

How do you think hypothesis testing helps in making decisions about a population based on sample data?

Multiple Choice

What is the main objective of hypothesis testing in statistics?

• To test claims about parameters based on a random sample

• To collect as much data as possible

• To prove a theory is always true

• To avoid making any decisions