Question 1

Which of the following scenarios is most appropriate for using a matched pairs (dependent samples) t-test?

Accepted Answer

Comparing the blood pressure of patients before and after taking medication.

Question 2

What is the null hypothesis $$H_0$$ when testing the mean difference in matched pairs?

Accepted Answer

$$H_0$$: \mu_d = 0$$

Question 3

Given $$n$$ pairs of matched data, the test statistic for the matched pairs t-test is:

Accepted Answer

$$t = \frac{\bar{d}}{s_d / \sqrt{n}}$$

Question 4

In a study, 20 students take a pre-test and a post-test. The differences in scores are calculated for each student. Which requirement must be met to use the matched pairs t-test?

Accepted Answer

The differences must be normally distributed.

Question 5

A researcher wants to estimate the mean difference in blood pressure before and after treatment. Which formula gives the confidence interval for the mean difference?

Accepted Answer

$$\bar{d} \pm t_{\alpha/2} \frac{s_d}{\sqrt{n}}$$

Question 6

Why is it important to always subtract in the same way (e.g., first value minus second) when calculating differences in matched pairs?

Accepted Answer

To maintain consistency and avoid bias in the direction of the mean difference.

Question 7

In the example comparing ages of actors and actresses, why is the matched pairs t-test appropriate?

Accepted Answer

Because each actor is paired with an actress by year, making the samples dependent.

Question 8

If the confidence interval for the mean difference in matched pairs is $$(-16.5, -2.9)$$, what conclusion can be drawn at the 0.05 significance level?

Accepted Answer

Reject $$H_0$$; there is significant evidence that the mean difference is less than zero.

Question 9

Which of the following is NOT a requirement for using the matched pairs t-test?

Accepted Answer

The two samples must be independent.

Question 10

A medical researcher collects before-and-after cholesterol levels for 35 patients. The sample mean difference is $$\bar{d} = -8 mg/dL$$, and the sample standard deviation of differences is $$s_d = 12 mg/dL. $$What is the value of the test statistic?

Accepted Answer

$$t = \frac{-8}{12 / \sqrt{35}}$$

Question 11

When using a matched pairs t-test, what does $$\mu_d$$ represent?

Accepted Answer

The mean of the differences for the population of all matched pairs.

Question 12

Which statement best describes the robustness of the matched pairs t-test?

Accepted Answer

It is robust if the sample size is at least 30, even if the differences are not perfectly normal.

Question 13

A psychologist wants to test if a new therapy reduces anxiety scores. She measures anxiety before and after therapy for each patient. What is the alternative hypothesis $$H_a if $$she expects a reduction?

Accepted Answer

$$H_a: \mu_d \u003c 0$$

Question 14

Which of the following is a correct step in the procedure for inference of matched pairs?

Accepted Answer

Verify that data comes from matched pairs and requirements are satisfied.

Question 15

In a matched pairs study, the sample mean of differences is $$\bar{d} = 2.5$$, the sample standard deviation is $$s_d = 4.0$$, and $$n = 16. $$What is the margin of error $$E$$ for a 95% confidence interval if $$t_{0.025, 15} = 2.131$$?

Accepted Answer

$$E = 2.131 	imes \frac{4.0}{\sqrt{16}}$$

Question 16

A study compares the effectiveness of two diets by measuring weight loss for each participant on both diets. Which statistical test should be used?

Accepted Answer

Matched pairs t-test

Question 17

If the p-value for a matched pairs t-test is 0.014 and the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence of a difference.

Question 18

Which of the following is a real-world example of matched pairs data?

Accepted Answer

Measuring the reaction time of drivers before and after drinking coffee.

Question 19

When calculating the test statistic for matched pairs, which value is used in the denominator?

Accepted Answer

$$s_d / \sqrt{n}$$

Two Dependent Samples (Matched Pairs): Hypothesis Testing and Confidence Intervals

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