Hypothesis Testing

Question 1

Which of the following best describes the null hypothesis?

A) The hypothesis that there is a significant effect.
B) The hypothesis that the results are due to chance.
C) The hypothesis that there is no significant difference.
D) The hypothesis that all sample means are equal.

Answer 1

C) The hypothesis that there is no significant difference.

Question 2

In a hypothesis test, if the p-value is less than the significance level (α), you should:

A) Fail to reject the null hypothesis.
B) Reject the null hypothesis.
C) Increase the sample size.
D) Change the significance level.

Answer 2

B) Reject the null hypothesis.

Question 3

A Type I error occurs when:

A) The null hypothesis is rejected when it is true.
B) The null hypothesis is not rejected when it is false.
C) The alternative hypothesis is accepted when it is false.
D) There is insufficient evidence to make a decision.

Answer 3

A) The null hypothesis is rejected when it is true.

Question 4

Which of the following tests is appropriate for comparing means of two independent samples?

A) Paired t-test
B) Independent t-test
C) Chi-square test
D) ANOVA

Answer 4

B) Independent t-test

Question 5

In hypothesis testing, the p-value represents:

A) The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.
B) The probability that the null hypothesis is true.
C) The probability that the alternative hypothesis is true.
D) The probability of making a Type II error.

Answer 5

A) The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

Question 6

The level of significance in hypothesis testing is typically denoted by:

A) β
B) α
C) p
D) µ

Answer 6

B) α

Question 7

A p-value of 0.03 means:

A) There is a 3% chance that the null hypothesis is true.
B) There is a 3% chance that the results are due to random variation.
C) There is a 97% chance that the null hypothesis is true.
D) The probability of observing the sample results, given that the null hypothesis is true, is 3%.

Answer 7

D) The probability of observing the sample results, given that the null hypothesis is true, is 3%.

Question 8

In an ANOVA test, the null hypothesis is:

A) The variances of the populations are equal.
B) The population means are equal.
C) The sample means are different.
D) The population variances are different.

Answer 8

B) The population means are equal.

Question 9

What does a chi-square test measure?

A) The mean difference between groups.
B) The association between categorical variables.
C) The probability of a continuous variable.
D) The difference between paired sample means.

Answer 9

B) The association between categorical variables.

Question 10

The power of a test is defined as:

A) The probability of rejecting the null hypothesis.
B) The probability of accepting the null hypothesis.
C) The probability of correctly rejecting a false null hypothesis.
D) The probability of making a Type I error.

Answer 10

C) The probability of correctly rejecting a false null hypothesis.

Question 11

A Type II error occurs when:

A) The null hypothesis is rejected when it is true.
B) The null hypothesis is not rejected when it is false.
C) The alternative hypothesis is rejected when it is false.
D) There is insufficient evidence to make a decision.

Answer 11

A) The null hypothesis is rejected when it is true.

Question 12

Which of the following would increase the power of a test?

A) Increasing sample size
B) Increasing significance level
C) Reducing variance
D) All of the above

Answer 12

D) All of the above

Question 13

When should you use a paired t-test?

A) Comparing two related groups
B) Comparing two independent groups
C) Comparing frequencies
D) Comparing variances

Answer 13

A) Comparing two related groups

Question 14

The F-distribution is used in which of the following tests?

A) Chi-square test
B) t-test
C) ANOVA
D) Z-test

Answer 14

C) ANOVA

Question 15

What is the critical value in hypothesis testing?

A) The probability of making a Type I error
B) The threshold to reject the null hypothesis
C) The value that must exceed the test statistic
D) The effect size needed to reject the null hypothesis

Answer 15

B) The threshold to reject the null hypothesis

Question 16

The null hypothesis is rejected when:

A) The p-value is greater than α
B) The test statistic is within the confidence interval
C) The p-value is less than α
D) The sample mean is equal to the population mean

Answer 16

C) The p-value is less than α

Question 17

Which of the following would decrease the likelihood of a Type I error?

A) Increasing sample size
B) Decreasing α
C) Increasing variance
D) Using a two-tailed test

Answer 17

B) Decreasing α

Question 18

What is the alternative hypothesis in a hypothesis test?

A) The hypothesis that predicts a difference
B) The hypothesis that predicts no difference
C) The hypothesis that the sample is biased
D) The hypothesis that the population mean is zero

Answer 18

A) The hypothesis that predicts a difference

Question 19

The Central Limit Theorem states that:

A) All sample distributions become normal
B) The distribution of sample means will be approximately normal, regardless of the population distribution, as sample size increases
C) The sample mean equals the population mean
D) Variance decreases with larger samples

Answer 19

B) The distribution of sample means will be approximately normal, regardless of the population distribution, as sample size increases

Question 20

In a hypothesis test, the test statistic measures:

A) The likelihood of a Type I error
B) The effect size
C) The amount of evidence against the null hypothesis
D) The variability of the sample

Answer 20

C) The amount of evidence against the null hypothesis

Question 21

Which distribution is used in a Z-test?

A) Normal distribution
B) t-distribution
C) Chi-square distribution
D) Exponential distribution

Answer 21

A) Normal distribution

Question 22

In hypothesis testing, if the confidence interval includes zero, this suggests:

A) The null hypothesis should be rejected
B) There is no significant difference
C) The sample mean is larger than the population mean
D) The test is invalid

Answer 22

B) There is no significant difference

Question 23

A two-tailed test is used when:

A) The test only evaluates one direction
B) The test evaluates two directions
C) The test is less powerful
D) The test has more Type I errors

Answer 23

B) The test evaluates two directions

Question 24

What is an effect size in hypothesis testing?

A) The probability of making a Type I error
B) The size of the effect of interest
C) The size of the sample
D) The amount of Type II error

Answer 24

B) The size of the effect of interest

Question 25

If the sample size increases, the p-value will:

A) Increase
B) Decrease
C) Stay the same
D) Be zero

Answer 25

A) Increase

Question 26

The t-test is suitable for:

A) Testing the difference between means
B) Testing the relationship between variables
C) Testing frequencies
D) Testing variances

Answer 26

A) Testing the difference between means

Question 27

When conducting a test for proportions, which condition must be met?

A) np ≥ 10 and n(1 − p) ≥ 10
B) np < 5
C) n > 30
D) n(1 − p) < 5

Answer 27

A) np ≥ 10 and n(1 − p) ≥ 10

Question 28

An increase in sample variance will:

A) Increase power
B) Increase Type I error
C) Decrease power
D) Decrease significance level

Answer 28

C) Decrease power

Question 29

Which of the following tests compares observed frequencies to expected frequencies?

A) Paired t-test
B) Chi-square test
C) Z-test
D) Mann-Whitney U test

Answer 29

B) Chi-square test