Hypothesis Testing: Master the Fundamentals of Statistical Inference

Question 1

What is the primary purpose of a p-value?

Accepted Answer

To determine the likelihood of observing the sample data assuming the null hypothesis is true.

Answer

To determine the probability of rejecting the null hypothesis when it is true.

Answer

To measure the statistical significance of the results.

Answer

To calculate the power of the hypothesis test.

Question 2

What does the power of a hypothesis test represent?

Accepted Answer

The probability of rejecting the null hypothesis when it is false.

Answer

The probability of accepting the null hypothesis when it is true.

Answer

The probability of making a Type I error.

Answer

The probability of making a Type II error.

Question 3

What is the purpose of a Bayes factor?

Accepted Answer

To compare the likelihood of competing hypotheses.

Answer

To determine the probability of observing the sample data assuming the null hypothesis is true.

Answer

To calculate the power of a hypothesis test.

Answer

To measure the statistical significance of the results.

Question 4

What does the Greek symbol α (alpha) represent in hypothesis testing?

Accepted Answer

The probability of making a Type I error

Answer

The probability of making a Type II error

Answer

The critical value of the test statistic

Answer

The p-value

Question 5

What is the critical value used for in hypothesis testing?

Accepted Answer

To establish the rejection region for the test statistic

Answer

To calculate the probability of making a Type I error

Answer

To determine the sample size required for the study

Answer

To interpret the results of the hypothesis test

Question 6

In hypothesis testing, what is the probability of rejecting the null hypothesis when it is true?

Accepted Answer

Type I error (α)

Answer

Type II error (β)

Answer

P-value

Question 7

Under which condition would you NOT reject the null hypothesis in hypothesis testing?

Accepted Answer

The p-value is greater than the significance level.

Answer

There is a statistically significant difference between the observed and expected results.

Answer

The sample size is small.

Answer

The null hypothesis is implausible.

Question 8

What is the definition of a p-value?

Accepted Answer

The probability of observing a test statistic as extreme or more extreme, assuming the null hypothesis is true

Answer

The probability of observing a test statistic as less extreme, assuming the null hypothesis is true

Answer

The probability of rejecting the null hypothesis

Answer

The probability of accepting the alternative hypothesis

Question 9

A researcher conducts a hypothesis test and obtains a p-value of 0.03. What is the appropriate conclusion at the 0.05 significance level?

Accepted Answer

Reject the null hypothesis

Answer

Fail to reject the null hypothesis

Answer

Increase the sample size

Answer

Conduct a further test

Question 10

What is the graphical representation of the distribution of a test statistic under the null hypothesis called?

Accepted Answer

Null distribution

Answer

Sampling distribution

Answer

Probability distribution

Answer

Standard normal distribution

Question 11

In hypothesis testing, the null hypothesis is primarily characterized by:

Accepted Answer

Being the hypothesis initially assumed to be true and tested against the alternative hypothesis

Answer

Always being a one-tailed hypothesis

Answer

Always being rejected if the p-value is less than the significance level

Question 12

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

Accepted Answer

Type III error

Answer

Type I error

Answer

Type II error

Question 13

What is the probability of rejecting a true null hypothesis?

Accepted Answer

Depends on the significance level

Answer

0

Answer

0.05

Question 14

What is the p-value in a hypothesis test?

Accepted Answer

The probability of observing the sample result assuming the null hypothesis is true

Answer

The probability of rejecting the null hypothesis

Question 15

What is the purpose of a one-tailed hypothesis test?

Accepted Answer

To test for a specific direction of an effect

Answer

To test for a difference in two means

Question 16

What is the null hypothesis in a hypothesis test?

Accepted Answer

The hypothesis that is assumed to be true before the test

Answer

The hypothesis that is supported by the data

Question 17

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

Accepted Answer

Rejecting the null hypothesis when it is true

Answer

Accepting the null hypothesis when it is false

Answer

Failing to reject the null hypothesis when it is false

Answer

Accepting the alternative hypothesis when it is true

Question 18

What does the p-value represent in hypothesis testing?

Accepted Answer

The probability of obtaining the observed results assuming the null hypothesis is true

Answer

The smallest significance level at which the null hypothesis can be rejected

Answer

The probability of accepting the null hypothesis

Answer

The difference between the observed and expected values

Question 19

What does committing a Type I error entail?

Accepted Answer

Rejecting H0 when it is true

Answer

Rejecting Ha when it is true

Answer

Accepting H0 when it is false

Answer

Accepting Ha when it is false

Question 20

Which of the following p-value values would provide the strongest evidence against the null hypothesis?

Accepted Answer

0.01

Answer

0.05

Answer

0.10

Answer

0.20

Question 21

In a right-tailed test, the critical value is located in the:

Accepted Answer

Right tail of the distribution

Answer

Left tail of the distribution

Answer

Both tails of the distribution

Answer

Center of the distribution

Question 22

What is the primary purpose of conducting a power analysis?

Accepted Answer

To determine the minimum sample size needed to achieve a desired level of statistical power

Answer

To calculate the p-value of a hypothesis test

Answer

To select the most appropriate statistical test for a given research question

Answer

To interpret the results of a confidence interval

Question 23

What is the interpretation of 'rejecting the null hypothesis' in hypothesis testing?

Accepted Answer

Providing strong evidence against the null hypothesis, suggesting that it is likely false

Answer

Providing definitive proof that the null hypothesis is false

Answer

Concluding with certainty that the alternative hypothesis is true

Answer

Accepting the null hypothesis

Question 24

What is the fundamental difference between a 'one-tailed' and a 'two-tailed' hypothesis test?

Accepted Answer

One-tailed tests test for a difference in one specific direction, while two-tailed tests test for a difference in either direction

Answer

Two-tailed tests test for a difference in one specific direction, while one-tailed tests test for a difference in either direction

Answer

One-tailed tests are more powerful than two-tailed tests

Answer

Two-tailed tests are more powerful than one-tailed tests

Question 25

What is the purpose of the alternative hypothesis in hypothesis testing?

Accepted Answer

To provide an alternative explanation for the observed data

Answer

To reject the null hypothesis

Answer

To determine the significance of the results

Answer

To calculate the p-value

Question 26

What is the relationship between the significance level and the p-value?

Accepted Answer

If the p-value is less than the significance level, the null hypothesis is rejected

Answer

If the significance level is less than the p-value, the null hypothesis is accepted

Answer

The significance level and the p-value are always equal

Answer

The significance level and the p-value are independent of each other

Question 27

What is the role of power analysis in hypothesis testing?

Accepted Answer

To determine the sample size needed to achieve a desired level of power

Answer

To calculate the p-value

Answer

To determine the significance level

Answer

To evaluate the accuracy of the results

Question 28

What is the purpose of the alpha level in hypothesis testing?

Accepted Answer

To control the probability of Type I error

Answer

To determine the critical value

Answer

To calculate the p-value

Answer

To estimate the effect size

Question 29

Which type of error occurs when we fail to reject the null hypothesis when it is actually false?

Accepted Answer

Type II error

Answer

Sampling error

Answer

Hypothesis error

Answer

Type I error

Question 30

Which symbol represents the alternative hypothesis?

Accepted Answer

Ha

Answer

H0

Answer

Hn

Answer

Hs

Question 31

What is the primary goal of a power analysis in hypothesis testing?

Accepted Answer

To determine the minimum sample size to achieve a desired statistical power

Answer

To choose the appropriate test statistic

Answer

To calculate the p-value

Question 32

Which of the following is a commonly used two-sample hypothesis test?

Accepted Answer

Two-sample t-test

Answer

Linear regression

Answer

ANOVA

Answer

Chi-square test

Question 33

In hypothesis testing, the significance level (α) represents the:

Accepted Answer

Probability of rejecting the null hypothesis when it is true (Type I error)

Answer

Probability of committing a Type II error

Answer

Probability of accepting the null hypothesis when it is true