Question 1

Which of the following best describes the main difference between Study A and Study B in the context of comparing purchase potential ratings before and after a commercial?

Accepted Answer

Study A uses different individuals for each group, while Study B uses the same individuals for both before and after ratings.

Question 2

What is a major flaw in Study A's design when comparing the effect of a commercial on purchase potential?

Accepted Answer

It cannot account for individual differences between the two groups.

Question 3

Which of the following is an advantage of using a paired sample (matched pairs) design in hypothesis testing?

Accepted Answer

It controls for individual variability by comparing each subject to themselves.

Question 4

Given the following before and after test scores for four employees: Sam (85, 94), Tamika (94, 87), Brian (78, 79), Mike (87, 88), what is the mean of the differences (After - Before)?

Accepted Answer

$$\frac{(94-85)+(87-94)+(79-78)+(88-87)}{4}$$

Question 5

Which formula would you use to calculate the 90% confidence interval for the mean difference $$\mu_d in a $$paired sample?

Accepted Answer

$$\bar{d} \pm t_{\alpha/2, n-1} \cdot \frac{s_d}{\sqrt{n}}$$

Question 6

If the 90% confidence interval for the mean difference in test scores is $$[1.5, 7.5]$$, what does this imply?

Accepted Answer

The mean test score after training is significantly higher than before training.

Question 7

Which of the following is the correct null hypothesis for a paired t-test comparing before and after means?

Accepted Answer

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

Question 8

A marketing analyst compares calculator prices at 8 stores for a client and a competitor. Which test is most appropriate?

Accepted Answer

Paired t-test

Question 9

Given paired price data for 8 stores, the mean difference is $$-2.25$$ with a standard deviation of $$1.0. $$What is the test statistic for testing $$H_0$$: \mu_d = 0$$ at $$\alpha = 0.01$$?

Accepted Answer

$$t = \frac{-2.25 - 0}{1.0/\sqrt{8}}$$

Question 10

If the p-value for a paired t-test is $$0.0005$$ and $$\alpha = 0.01$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is a significant difference.

Question 11

Which assumption is required for valid inference about the mean difference $$\mu_d in a $$paired t-test with a small sample?

Accepted Answer

The differences are approximately normally distributed.

Question 12

In a paired t-test, what does it mean if the confidence interval for $$\mu_d$$ includes 0?

Accepted Answer

There is no significant difference between the paired means.

Question 13

Which of the following best describes the research question in a before-and-after study design?

Accepted Answer

Is there a significant change in the mean response after the intervention?

Question 14

When using Excel to perform a paired t-test, which option should you select in the Data Analysis Toolpak?

Accepted Answer

t-Test: Paired Two Sample for Means

Question 15

If the calculated t-statistic is less than the negative critical value in a left-tailed paired t-test, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 16

Which of the following is NOT a condition for valid large-sample inference about $$\mu_d$$?

Accepted Answer

The two samples are independent.

Question 17

A 99% confidence interval for the mean difference in calculator prices is $$[-3.5, -1.0]. $$What does this indicate?

Accepted Answer

The client's calculator is significantly less expensive than the competitor's.

Question 18

Which of the following best explains why paired samples are preferred over independent samples in before-and-after studies?

Accepted Answer

Paired samples control for individual differences, increasing statistical power.

Ch 8

Study Guide - Practice Questions

Study Guide - Flashcards