Hypothesis Testing FKEE

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

Arrange the steps involved in hypothesis testing in the correct order.

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

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

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

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

Multiple Select

Which of the following statements about hypotheses is/are correct?

• The null hypothesis is assumed true unless strong evidence is provided.

• The alternative hypothesis is accepted if the null hypothesis is rejected.

• A hypothesis is a statement about a population.

• All of the above.

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

Multiple Choice

Which of the following statements about test statistics is correct?

• Test statistics are only used to compare two sample means.

• Test statistics help decide whether to reject or fail to reject the null hypothesis.

• Test statistics are not related to hypothesis testing.

• Test statistics are used only for qualitative data.

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

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 Choice

In the context of a medical test, what would a Type I error imply?

• A healthy person is diagnosed as sick

• A sick person is diagnosed as healthy

• A healthy person is correctly diagnosed as healthy

• A sick person is correctly diagnosed as sick

Multiple Choice

In the context of a medical test, what would a Type II error imply?

• A healthy person is diagnosed as sick

• A sick person is diagnosed as healthy

• A healthy person is correctly diagnosed as healthy

• A sick person is correctly diagnosed as sick

Multiple Choice

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

• Rejecting a true null hypothesis

• Accepting a false null hypothesis

• Rejecting a false null hypothesis

• Accepting a true null hypothesis

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 is an example of a Type II error?

• Rejecting a true null hypothesis.

• Failing to reject a false null hypothesis.

• Accepting a true null hypothesis.

• Rejecting a false null hypothesis.

Multiple Select

Which statements about Type I error are correct?

• It occurs when a true null hypothesis is rejected

• It is also known as a false positive

• It means claiming a relationship exists when it does not

• It occurs when a false null hypothesis is accepted

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

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

Which type of hypothesis test is used to detect the difference between the parameters of two populations (μ₁ and μ₂)?

• One sample

• Two sample

• Paired sample

• Single mean

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 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.

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

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

Multiple Choice

Which of the following statements correctly describes a two-tailed hypothesis test for a single mean?

• It tests if the mean is greater than a specified value.

• It tests if the mean is less than a specified value.

• It tests if the mean is either greater or less than a specified value.

• It tests if the mean is different from a specified value.

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.

Multiple Choice

Which distribution is commonly used for hypothesis testing of a single variance?

• Z distribution

• T distribution

• χ₂ distribution

• F distribution