Comparing Means 2

Question 1

What type of experimental design is used with a paired-samples t-test?

1) Between-subjects design
2) Within-subjects design
3) Cross-sectional design
4) Matched-groups design

Answer 1

Within-subjects design

Question 2

What is the primary advantage of a paired-samples t-test over an independent samples t-test?

1) It does not require a normal distribution of data
2) It reduces error by comparing the same participants across conditions
3) It can compare more than two groups simultaneously
4) It uses a larger sample size to detect effects

Answer 2

It reduces error by comparing the same participants across conditions

Question 3

What does the paired-samples t-test compare?

1) Two unrelated groups with different participants
2) Two sets of means from the same participants at different times
3) A sample mean to a population mean
4) The variance within a single sample

Answer 3

Two sets of means from the same participants at different times

Question 4

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

1) There is a significant difference between the two sample means
2) The mean difference between paired scores is equal to zero
3) The sample mean is equal to the population mean
4) The standard deviation of the samples is significantly different

Answer 4

The mean difference between paired scores is equal to zero

Question 5

Which of the following is NOT an assumption of a paired-samples t-test?

1) Data is measured on an interval or ratio scale
2) The differences between paired scores are normally distributed
3) Both samples have equal variances
4) The sample is randomly selected from the population

Answer 5

Both samples have equal variances

Question 6

What does the t-statistic represent in a paired-samples t-test?

1) The standard deviation of the sampling distribution
2) The number of standard errors the mean difference is from zero
3) The variability within the two samples
4) The likelihood of a Type I error

Answer 6

The number of standard errors the mean difference is from zero

Question 7

What is the significance threshold for most paired-samples t-tests?

1) p < 0.10
2) p < 0.05
3) p < 0.01
4) p ≥ 0.05

Answer 7

p < 0.05

Question 8

What is the equation for calculating the degrees of freedom in a paired-samples t-test?

1) df = n1 + n2 - 2
2) df = n - 1
3) df = (n1 + n2) - 1
4) df = n1 + n2

Answer 8

df = n - 1

Question 9

What does a significant p-value in a paired-samples t-test indicate?

1) The mean difference is likely due to chance
2) The mean difference is significantly different from zero in the population
3) The null hypothesis cannot be rejected
4) There is no effect in the population

Answer 9

The mean difference is significantly different from zero in the population

Question 10

What is a one-sample t-test used for?

1) Comparing two unrelated groups
2) Comparing a sample mean to a known test value
3) Comparing two paired scores from the same sample
4) Determining whether variances are equal between groups

Answer 10

Comparing a sample mean to a known test value

Question 11

What is the null hypothesis for a one-sample t-test?

1) The sample mean is significantly different from the test value
2) The sample mean is equal to the test value
3) There is no variance within the sample
4) The sample is not representative of the population

Answer 11

The sample mean is equal to the test value

Question 12

What does a t-statistic of -14.71 in a one-sample t-test imply?
1) The sample mean is significantly larger than the test value
2) The sample mean is significantly smaller than the test value
3) There is no difference between the sample mean and test value
4) The data violates the assumptions of the t-test

Answer 12

The sample mean is significantly smaller than the test value

Question 13

What is a key difference between a paired-samples t-test and a one-sample t-test?

1) A paired-samples t-test compares means from two groups, while a one-sample t-test compares a mean to a single value
2) A paired-samples t-test uses fewer assumptions than a one-sample t-test
3) A one-sample t-test can only be used with interval data, while a paired-samples t-test cannot
4) A paired-samples t-test measures variance, while a one-sample t-test measures correlation

Answer 13

A paired-samples t-test compares means from two groups, while a one-sample t-test compares a mean to a single value

Question 14

When reporting paired-samples t-test results, which of the following should be included?

1) The exact p-value, t-statistic, degrees of freedom, and means of the groups
2) Only the t-statistic and the means of the groups
3) The p-value and standard deviation of each sample
4) Only the confidence interval of the mean difference

Answer 14

The exact p-value, t-statistic, degrees of freedom, and means of the groups

Question 15

What does “related-samples t-test” refer to?

1) A t-test comparing unrelated groups
2) Another name for the paired-samples t-test
3) A t-test for comparing a sample to a population
4) A t-test used for matched pairs only

Answer 15

Another name for the paired-samples t-test

Question 16

What happens to the standard error as sample size increases?

1) It increases
2) It decreases
3) It remains constant
4) It depends on the variability of the data

Answer 16

It decreases

Question 17

Why are paired-samples t-tests considered more powerful than independent samples t-tests?

1) They use more participants in each condition
2) They control for individual differences by measuring the same participants
3) They require fewer assumptions about the data
4) They automatically account for unequal variances

Answer 17

They control for individual differences by measuring the same participants

Question 18

What is a “critical region” in hypothesis testing?

1) The area where the null hypothesis is likely to be true
2) The range of values that leads to rejection of the null hypothesis
3) The calculated mean difference between two samples
4) The p-value at which the test is conducted

Answer 18

The range of values that leads to rejection of the null hypothesis

Question 19

Which test should be used to determine if the average score of a sample differs from a fixed population mean?

1) Independent samples t-test
2) Paired-samples t-test
3) One-sample t-test
4) Two-way ANOVA

Answer 19

One-sample t-test

Question 20

What does “t(99) = -14.71, p < 0.01” indicate in a one-sample t-test report?

1) The sample size was 99
2) The degrees of freedom were 99, and the mean difference was statistically significant
3) The t-statistic was calculated incorrectly
4) The null hypothesis cannot be rejected

Answer 20

The degrees of freedom were 99, and the mean difference was statistically significant