D3 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

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

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

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

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

Question 6

When performing a hypothesis test for a population proportion, which distribution is generally used?

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

Answer 6

A

Question 7

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

A) β
B) α
C) p
D) µ

Answer 7

B

Question 8

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 8

D

Question 9

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 9

B

Question 10

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 10

B

Question 11

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 11

C

Question 12

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 12

A

Question 13

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 13

D

Question 14

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 14

A

Question 15

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

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

Answer 15

C

Question 16

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 16

B

Question 17

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 17

C

Question 18

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 18

B

Question 19

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 19

A

Question 20

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 20

B

Question 21

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 21

C

Question 22

Which distribution is used in a Z-test?

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

Answer 22

A

Question 23

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 23

B

Question 24

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 24

B

Question 25

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 25

B

Question 26

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

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

Answer 26

A

Question 27

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 27

A

Question 28

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 28

A

Question 29

An increase in sample variance will:
A) Increase power
B) Increase Type I error
C) Decrease power
D) Decrease significance level

Answer 29

C

Question 30

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 30

B