T-Tests: A Comprehensive Guide for Psychology Students

Question 1

Which of the following is the primary purpose of a one-sample t-test?

Accepted Answer

To compare the mean of a sample to a known population mean.

Answer

To compare the means of two independent samples.

Answer

To determine if the population distribution is normally distributed.

Answer

To test for equality of variances between two groups.

Question 2

What is the formula for calculating the degrees of freedom for a two-sample t-test?

Accepted Answer

n1 + n2 - 2

Answer

n1 - 1

Answer

n2 - 1

Answer

The smaller of n1 and n2.

Question 3

What is the null hypothesis for a paired t-test?

Accepted Answer

The mean difference between the two groups is zero.

Answer

The mean of Group 1 is greater than the mean of Group 2.

Answer

The mean of Group 1 is less than the mean of Group 2.

Answer

The means of the two groups are different.

Question 4

What is the purpose of a confidence interval in a t-test?

Accepted Answer

To provide an estimate of the population mean with a margin of error.

Answer

To determine the significance of the test result.

Answer

To control for the effects of confounding variables.

Answer

To test for normality in the population distribution.

Question 5

A researcher obtains a t-statistic of -2.262 from a one-sample t-test with a sample size of 25. Assuming a significance level of 0.05, what is the p-value?

Accepted Answer

0.02

Answer

0.05

Answer

0.10

Answer

0.15

Question 6

Which of the following assumptions is not required for a t-test?

Accepted Answer

The variances of the two groups being compared are equal.

Answer

The population distribution is normally distributed.

Answer

The sample is randomly selected.

Answer

The sample size is large enough.

Question 7

The p-value in a t-test represents:

Accepted Answer

The probability of obtaining a t-value as extreme as or more extreme than the observed t-value, assuming the null hypothesis is true.

Answer

The probability of obtaining a sample mean as extreme as or more extreme than the observed sample mean, assuming the null hypothesis is true.

Answer

The probability of rejecting the null hypothesis, given that it is true.

Answer

The probability of accepting the null hypothesis, given that it is false.

Question 8

The effect size in a t-test measures the:

Accepted Answer

Magnitude of the effect being tested.

Answer

Probability of making a Type I error.

Answer

Difference between the sample mean and the hypothesized mean.

Answer

Number of participants in the study.

Question 9

A key limitation of t-tests is their:

Accepted Answer

Sensitivity to violations of assumptions.

Answer

Requirement for large sample sizes.

Answer

Inability to test for relationships between variables.

Answer

Inability to compare more than two groups.

Question 10

The fundamental difference between a one-sample and a two-sample t-test lies in:

Accepted Answer

Comparing a sample mean to a hypothesized mean versus comparing two sample means.

Answer

Assumptions of normality and independence.

Answer

Formula used to calculate degrees of freedom.

Answer

Type of research question being addressed.

Question 11

When conducting a one-sample t-test, the null hypothesis states that:

Accepted Answer

The population mean is not different from zero.

Answer

The population mean is different from zero.

Answer

The sample mean is different from zero.

Answer

The sample mean is equal to zero.

Question 12

Which of the following effect sizes is considered large for a t-test?

Accepted Answer

0.80

Answer

0.10

Answer

0.30

Answer

0.50

Question 13

A researcher conducts a two-sample t-test and finds a significant difference between the means of the two groups. Which of the following conclusions is NOT valid?

Accepted Answer

The difference between the means is clinically significant.

Answer

The null hypothesis is rejected.

Answer

The alternative hypothesis is supported.

Answer

The two groups are statistically different.

Question 14

In comparing the means of two statistically independent groups, which t-test is the most appropriate?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Paired t-test

Answer

Chi-square test

Question 15

For a one-sample t-test, what is the null hypothesis?

Accepted Answer

The sample mean is not significantly different from the hypothesized mean.

Answer

The sample mean is significantly different from the hypothesized mean.

Answer

The sample is normally distributed.

Answer

The population variance is equal to the hypothesized variance.

Question 16

What is the primary purpose of a paired t-test?

Accepted Answer

To compare the means of two related groups.

Answer

To compare the means of two independent groups.

Answer

To assess the variance between two groups.

Answer

To determine the correlation between two variables.

Question 17

When comparing the means of three or more groups, which statistical test is most appropriate?

Accepted Answer

Analysis of variance (ANOVA)

Answer

One-sample t-test

Answer

Two-sample t-test

Answer

Paired t-test

Question 18

What is the primary role of confidence intervals in t-tests?

Accepted Answer

To estimate the range of possible population means.

Answer

To determine the rejection of the null hypothesis.

Answer

To calculate the sample size.

Answer

To identify outliers in the data.

Question 19

In a one-sample t-test, the null hypothesis proposes that:

Accepted Answer

The population mean is equal to the hypothesized value.

Answer

The population mean is different from the hypothesized value.

Answer

The sample mean is greater than the hypothesized value.

Answer

The sample mean is less than the hypothesized value.

Question 20

Which of the following is a crucial assumption of the paired t-test?

Accepted Answer

The differences between the pairs are normally distributed.

Answer

The data is normally distributed.

Answer

The data points are independent of each other.

Answer

The variances of the two groups are equal.

Question 21

The effect size for a t-test comparing the means of two independent groups is calculated as:

Accepted Answer

Difference between the means divided by the pooled standard deviation

Answer

Mean difference divided by the standard deviation of the difference

Answer

T-value divided by the degrees of freedom

Answer

F-value divided by the p-value

Question 22

A potential limitation of t-tests is that they:

Accepted Answer

Assume normal distribution of the data.

Answer

Can only be used with large sample sizes.

Answer

Are not sensitive to outliers.

Answer

Cannot be used to compare more than two groups.

Question 23

In a paired t-test comparing mean scores before and after an intervention, the null hypothesis states that:

Accepted Answer

The mean difference between the scores is zero.

Answer

The mean score before the intervention is greater than the mean score after the intervention.

Answer

The mean score after the intervention is greater than the mean score before the intervention.

Answer

The mean scores are not equal.

Question 24

When comparing the means of two independent groups with unequal variances, which t-test is most appropriate?

Accepted Answer

Welch's t-test

Answer

Student's t-test (assuming equal variances)

Answer

Paired t-test

Answer

ANOVA

Question 25

Which scenario would be most suitable for using a paired t-test?

Accepted Answer

Comparing the mean weights of participants in a diet program before and after the program.

Answer

Comparing the mean heights of male and female students in a class.

Answer

Comparing the mean test scores of two different classes.

Answer

Comparing the mean incomes of people living in two different cities.

Question 26

When conducting a two-sample t-test, which assumption is essential to ensure the validity of the analysis?

Accepted Answer

A. Equal variances (homoscedasticity) of the two populations

Answer

B. Normal distribution of data in both populations

Answer

C. Extremely large sample sizes

Answer

D. Dependent (paired) samples

Question 27

Which of the following is NOT a type of t-test used in statistics?

Accepted Answer

F-test

Answer

One-sample t-test

Answer

Paired t-test

Answer

Two-sample t-test

Question 28

What is the purpose of a one-sample t-test?

Accepted Answer

To determine if the mean of a sample is significantly different from a specified value.

Answer

To test the significance of a correlation.

Answer

To compare the means of two paired samples.

Answer

To compare the means of two independent samples.

Question 29

When conducting a two-sample t-test, which assumption is crucial and often tested?

Accepted Answer

The variances of the two populations being compared are equal.

Answer

The sample sizes are equal.

Answer

The data is independent.

Answer

The samples are normally distributed.

Question 30

What is a key benefit of using a paired t-test?

Accepted Answer

It controls for individual differences within the same subjects.

Answer

It increases the sample size.

Answer

It is more powerful than a one-sample t-test.

Answer

It reduces the variability of the data.

Question 31

Provide an example of a practical application of a t-test.

Accepted Answer

Comparing the effectiveness of two different teaching methods.

Answer

Testing the reliability of a measurement scale.

Answer

Predicting the future value of a stock.

Question 32

To examine if a new learning intervention enhances IQ scores compared to a known population mean of 100, which t-test would be suitable?

Accepted Answer

One-sample t-test

Answer

Paired t-test

Answer

Independent-samples t-test

Answer

Two-sample t-test

Question 33

A study measures anxiety levels before and after a therapy. Which t-test is appropriate for analyzing the difference in anxiety scores?

Accepted Answer

Paired t-test

Answer

Two-tailed t-test

Answer

Independent-samples t-test

Answer

One-sample t-test

Question 34

A researcher compares the average reaction times of two groups, one exposed to a stimulant and the other to a placebo. What type of t-test is most suitable?

Accepted Answer

Independent-samples t-test

Answer

Paired t-test

Answer

One-sample t-test

Question 35

In a one-sample t-test, what is the null hypothesis?

Accepted Answer

The sample mean is equal to the population mean.

Answer

The sample mean is significantly different from the population mean.

Answer

The sample mean is greater than the population mean.

Question 36

Which factor primarily influences the degrees of freedom in a t-test?

Accepted Answer

Sample size

Answer

Mean difference

Answer

Population size

Answer

Standard deviation

Question 37

A researcher conducts a two-sample t-test and obtains a p-value of 0.03. Based on this p-value, what can be concluded?

Accepted Answer

The results are statistically significant, rejecting the null hypothesis.

Answer

The results are not statistically significant, failing to reject the null hypothesis.

Answer

The sample sizes are too small to draw any conclusions.

Question 38

What is the role of the critical value in a t-test?

Accepted Answer

It determines the boundary between statistically significant and non-significant results.

Answer

It represents the mean difference between the groups.

Question 39

A researcher investigates the effect of a medication on sleep quality using a randomized controlled trial. What type of t-test is appropriate for analyzing the difference in sleep quality scores?

Accepted Answer

Independent-samples t-test

Answer

One-sample t-test

Answer

Two-tailed t-test

Answer

Paired t-test