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Hypothesis Testing

Description: This quiz is designed to test your understanding of the fundamental concepts and techniques of Hypothesis Testing, a crucial component of inferential statistics. The questions cover various aspects of hypothesis testing, including formulating hypotheses, selecting appropriate tests, interpreting results, and making statistical inferences.
Number of Questions: 15
Created by:
Tags: hypothesis testing statistical inference null hypothesis alternative hypothesis type i error type ii error p-value significance level statistical power
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In hypothesis testing, what is the probability of rejecting the null hypothesis when it is actually true?

  1. Type I Error

  2. Type II Error

  3. P-value

  4. Significance Level

Show answer
Correct Option: A
Explanation:

Type I error is the probability of rejecting the null hypothesis when it is actually true. It is also known as the false positive rate.

What is the probability of failing to reject the null hypothesis when it is actually false?

  1. Type I Error

  2. Type II Error

  3. P-value

  4. Significance Level

Show answer
Correct Option: B
Explanation:

Type II error is the probability of failing to reject the null hypothesis when it is actually false. It is also known as the false negative rate.

In hypothesis testing, the significance level is the probability of:

  1. Rejecting the null hypothesis when it is true

  2. Failing to reject the null hypothesis when it is false

  3. Making a correct decision

  4. Making an incorrect decision

Show answer
Correct Option: A
Explanation:

The significance level is the probability of rejecting the null hypothesis when it is actually true. It is also known as the alpha level.

The p-value is the probability of:

  1. Rejecting the null hypothesis when it is true

  2. Failing to reject the null hypothesis when it is false

  3. Making a correct decision

  4. Making an incorrect decision

Show answer
Correct Option:
Explanation:

The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed test statistic, assuming the null hypothesis is true.

If the p-value is less than the significance level, then:

  1. We reject the null hypothesis

  2. We fail to reject the null hypothesis

  3. We make a correct decision

  4. We make an incorrect decision

Show answer
Correct Option: A
Explanation:

If the p-value is less than the significance level, then we reject the null hypothesis.

If the p-value is greater than the significance level, then:

  1. We reject the null hypothesis

  2. We fail to reject the null hypothesis

  3. We make a correct decision

  4. We make an incorrect decision

Show answer
Correct Option: B
Explanation:

If the p-value is greater than the significance level, then we fail to reject the null hypothesis.

The power of a hypothesis test is the probability of:

  1. Rejecting the null hypothesis when it is true

  2. Failing to reject the null hypothesis when it is false

  3. Making a correct decision

  4. Making an incorrect decision

Show answer
Correct Option:
Explanation:

The power of a hypothesis test is the probability of rejecting the null hypothesis when it is actually false.

Which of the following is NOT a type of hypothesis testing?

  1. One-sample t-test

  2. Two-sample t-test

  3. Analysis of variance (ANOVA)

  4. Regression analysis

Show answer
Correct Option: D
Explanation:

Regression analysis is not a type of hypothesis testing. It is a statistical method used to determine the relationship between one or more independent variables and a dependent variable.

In a two-sample t-test, the null hypothesis is that:

  1. The means of the two populations are equal

  2. The means of the two populations are different

  3. The variances of the two populations are equal

  4. The variances of the two populations are different

Show answer
Correct Option: A
Explanation:

In a two-sample t-test, the null hypothesis is that the means of the two populations are equal.

In an analysis of variance (ANOVA), the null hypothesis is that:

  1. The means of all the groups are equal

  2. The means of some of the groups are different

  3. The variances of all the groups are equal

  4. The variances of some of the groups are different

Show answer
Correct Option: A
Explanation:

In an analysis of variance (ANOVA), the null hypothesis is that the means of all the groups are equal.

Which of the following is NOT a type of statistical power analysis?

  1. A priori power analysis

  2. Post hoc power analysis

  3. Sensitivity analysis

  4. Meta-analysis

Show answer
Correct Option: D
Explanation:

Meta-analysis is not a type of statistical power analysis. It is a statistical method used to combine the results of multiple studies.

Which of the following is NOT a common misconception about hypothesis testing?

  1. The p-value is the probability of the null hypothesis being true

  2. The significance level is the probability of making a Type I error

  3. The power of a hypothesis test is the probability of making a Type II error

  4. Hypothesis testing is always a binary decision

Show answer
Correct Option: D
Explanation:

Hypothesis testing is not always a binary decision. In some cases, we may have more than two hypotheses or we may need to consider the magnitude of the effect.

Which of the following is NOT a good practice in hypothesis testing?

  1. Clearly stating the null and alternative hypotheses

  2. Selecting an appropriate statistical test

  3. Interpreting the results of the hypothesis test in the context of the research question

  4. Changing the significance level after seeing the results of the hypothesis test

Show answer
Correct Option: D
Explanation:

Changing the significance level after seeing the results of the hypothesis test is a bad practice. It is known as p-hacking and it can lead to misleading results.

Which of the following is NOT a common type of hypothesis testing error?

  1. Type I error

  2. Type II error

  3. Type III error

  4. Type IV error

Show answer
Correct Option: D
Explanation:

Type IV error is not a common type of hypothesis testing error. It is a term sometimes used to refer to the error of rejecting the null hypothesis when it is actually true, but the alternative hypothesis is not supported by the data.

Which of the following is NOT a common method for controlling the family-wise error rate (FWER) in multiple hypothesis testing?

  1. Bonferroni correction

  2. Holm-Bonferroni correction

  3. Sidak correction

  4. Tukey's Honestly Significant Difference (HSD) test

Show answer
Correct Option: D
Explanation:

Tukey's Honestly Significant Difference (HSD) test is a multiple comparison procedure, but it is not a method for controlling the family-wise error rate (FWER). It is used to control the experiment-wise error rate (EWER).

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