Question 1

Which of the following scenarios best describes paired data?

Accepted Answer

Measuring the blood pressure of 20 patients before and after administering a new drug.

Question 2

What is the primary reason for using a paired t-test instead of a two-sample t-test?

Accepted Answer

To account for the natural pairing or matching between observations, reducing extra variation.

Question 3

Given the following hypotheses for a paired t-test: $$H_0$$: \mu_d = 0$$ and H_a$$: \mu_d 
eq 0$$, what does $$\mu_d$$ represent?

Accepted Answer

$$\mu_d is $$the mean of the pairwise differences between the two related samples.

Question 4

A researcher measures water clarity at the same location in a lake on the same dates in 2015 and again in 2020. Which statistical test is most appropriate to determine if water clarity has changed?

Accepted Answer

A paired t-test, because the measurements are naturally paired by location and date.

Question 5

Which of the following is NOT an assumption or condition for the paired t-test?

Accepted Answer

The original samples must be independent of each other.

Question 6

Suppose you have $$n$$ pairs of observations. What is the correct formula for the test statistic in a paired t-test?

Accepted Answer

$$t = \frac{\bar{d} - \$$Delta_0$$}{\frac{s_d}{\sqrt{n}}}$$

Question 7

In the context of a paired t-test, what does the sample size $$n$$ refer to?

Accepted Answer

The number of pairs of observations.

Question 8

A study compares the reaction times of participants to a blue screen and a red screen. Each participant is tested under both conditions. What is the main advantage of this paired design?

Accepted Answer

It controls for individual differences by comparing each participant to themselves.

Question 9

Which of the following best describes the purpose of blocking in experimental design?

Accepted Answer

To reduce variation by grouping similar experimental units together.

Question 10

If the 99% confidence interval for the mean difference in a paired t-test is $$(-0.309, 0.543)$$, what can you conclude?

Accepted Answer

There is no significant difference between the two groups at the 1% significance level.

Question 11

Which of the following is a common mistake when analyzing paired data?

Accepted Answer

Using a two-sample t-test instead of a paired t-test.

Question 12

A paired t-test is performed and the p-value is 0.024. If $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

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

Question 13

Which formula gives the $$(1-\alpha)100\%$$ confidence interval for the mean difference $$\mu_d in $$paired data?

Accepted Answer

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

Question 14

Why is it incorrect to use side-by-side boxplots of the two groups when analyzing paired data?

Accepted Answer

Because the analysis should focus on the distribution of the differences, not the original groups.

Question 15

In a paired t-test, what is the effect of pairing on the degrees of freedom compared to a two-sample t-test?

Accepted Answer

Pairing results in roughly half the degrees of freedom, but usually reduces extra variation.

Question 16

A biologist wants to estimate the mean difference in age between husbands and wives. Why is it important to use paired analysis?

Accepted Answer

Because each husband-wife pair forms a natural block, and the analysis should focus on the difference within each pair.

Question 17

Which of the following is a correct step when using software (like Minitab) to perform a paired t-test?

Accepted Answer

Calculate the differences between paired observations and use these differences for the test.

Question 18

If the boxplot of the differences in a paired t-test appears skewed, what should you do?

Accepted Answer

Check the normality of the differences using a normal probability plot or a formal test.

Question 19

A paired t-test is performed to compare two devices measuring the same quantity. The p-value is 0.413 and $$\alpha = 0.01. $$What is the correct interpretation?

Accepted Answer

There is no significant difference between the devices at the 1% significance level.

Paired Samples and Blocks: Inference for Dependent Samples

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