T-tests: A Comprehensive Guide for Data Analysis PhD Students

Question 1

How do you find the critical value for a t-test with a significance level of 0.05 and a sample size of 20?

Accepted Answer

Use a t-table with 19 degrees of freedom.

Answer

Use a normal distribution table with a mean of 0 and a standard deviation of 1.

Answer

Divide the significance level by the sample size.

Answer

Multiply the significance level by the sample size.

Question 2

What is the main difference between a one-tailed and a two-tailed t-test?

Accepted Answer

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

Answer

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

Answer

One-tailed tests require a smaller sample size than two-tailed tests.

Answer

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

Question 3

Which type of t-test is used for comparing means of paired data?

Accepted Answer

Dependent-samples t-test

Answer

Independent-samples t-test

Answer

One-sample t-test

Answer

Two-sample t-test

Question 4

How do you calculate the p-value for a t-test with a test statistic of -2.576 and a sample size of 20?

Accepted Answer

Use a t-table with 19 degrees of freedom.

Answer

Use a normal distribution table with a mean of 0 and a standard deviation of 1.

Answer

Multiply the test statistic by the sample size.

Answer

Divide the test statistic by the sample size.

Question 5

Which of the following is a common application of a t-test?

Accepted Answer

Comparing the means of two independent groups.

Answer

Testing the significance of a correlation coefficient.

Answer

Predicting the outcome of a regression analysis.

Answer

Estimating the proportion of a population.

Question 6

Which of the following is a violation of the normality assumption of a t-test?

Accepted Answer

The distribution of the data is skewed.

Answer

The sample size is small (n < 30).

Answer

The population variance is known.

Answer

The sample is randomly selected.

Question 7

Which non-parametric test is an alternative to the two-sample t-test for comparing medians?

Accepted Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Answer

Spearman's rank correlation coefficient

Question 8

What is the main purpose of a power analysis in the context of t-tests?

Accepted Answer

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

Answer

To calculate the probability of rejecting the null hypothesis when it is false.

Answer

To find the critical value for a given significance level.

Answer

To estimate the effect size of a study.

Question 9

When the sample size is less than 30, which non-parametric test can be used as an alternative to a one-sample t-test?

Accepted Answer

Wilcoxon signed-rank test

Answer

Two-sample t-test

Answer

Kruskal-Wallis test

Answer

Mann-Whitney U test

Question 10

Which of the following is NOT a type of two-sample t-test?

Accepted Answer

Hotelling's T-squared test

Answer

Independent samples t-test

Answer

Paired samples t-test

Answer

Welch's t-test

Question 11

What does a p-value less than 0.05 indicate in a t-test?

Accepted Answer

There is a statistically significant difference between the means.

Answer

There is no statistically significant difference between the means.

Answer

The data is normally distributed.

Answer

The sample size is large enough.

Question 12

How does increasing the sample size affect the power of a t-test?

Accepted Answer

Increases the power

Answer

Decreases the power

Answer

Does not affect the power

Answer

Increases the p-value

Question 13

Provide the formula for calculating the t-statistic for a one-sample t-test.

Accepted Answer

t = (Xbar - mu) / (s / sqrt(n))

Answer

t = (Xbar - mu) / sqrt(s^2 / n)

Answer

t = (Xbar - mu) * sqrt(n) / s

Answer

t = (Xbar - mu) * s / sqrt(n)

Question 14

Which of the following is an essential assumption of the one-sample t-test?

Accepted Answer

The population from which the sample was drawn is approximately normally distributed.

Answer

The population variance is known.

Answer

The sample size consists of at least 30 subjects.

Question 15

When is a two-sample t-test appropriate for use?

Accepted Answer

To compare the means of two independent groups.

Answer

To compare the variances of two populations.

Answer

To test the equality of proportions between two groups.

Question 16

In conducting a two-sample t-test with unequal variances, which test statistic should be used?

Accepted Answer

Welch's t-test statistic

Answer

Chi-square test statistic

Answer

Student's t-test statistic

Question 17

For a two-tailed t-test with a significance level of 0.05 and degrees of freedom (df) equal to 30, what is the critical value?

Accepted Answer

2.042

Answer

1.960

Answer

2.262

Question 18

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

Accepted Answer

The two population means are equal.

Answer

The sample sizes of the two groups are equal.

Answer

The two groups come from the same population.

Question 19

Which effect size measure is used in t-tests?

Accepted Answer

Cohen's d

Answer

Omega-squared

Answer

Pearson's r

Question 20

Which of the following illustrates a practical application of the t-test?

Accepted Answer

Comparing the effectiveness of two different educational interventions.

Answer

Estimating the population mean IQ score.

Answer

Analyzing the correlation between height and weight.