Question 1

Which of the following is a necessary condition for conducting a t-test for the difference between means with dependent samples?

Accepted Answer

The samples must be randomly selected and paired.

Question 2

What is the null hypothesis $$H_0$$ when testing if a treatment has an effect using paired data?

Accepted Answer

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

Question 3

A researcher wants to test if a new medication changes blood pressure. She measures blood pressure before and after treatment in 20 patients. Which test should she use?

Accepted Answer

Paired (dependent) samples t-test

Question 4

Given $$n$$ pairs of data, the test statistic for the paired t-test is calculated as:

Accepted Answer

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

Question 5

In a paired t-test, what does $$\bar{d}$$ represent?

Accepted Answer

The mean of the differences between paired observations

Question 6

A golf company claims lessons improve scores. Eight golfers’ scores before and after lessons are compared. If the calculated t-statistic does not fall in the rejection region, what is the correct conclusion at $$\alpha = 0.10$$?

Accepted Answer

Fail to reject the null hypothesis; no evidence lessons improve scores.

Question 7

Which of the following scenarios is most appropriate for a paired t-test?

Accepted Answer

Comparing cholesterol levels before and after a diet in the same group of patients.

Question 8

If the number of pairs $$n is $$less than 30, which assumption must be checked before using the paired t-test?

Accepted Answer

The differences are normally distributed.

Question 9

A legislator’s performance rating is measured for 16 voters last year and this year. The test is two-tailed at $$\alpha = 0.05. $$What is the alternative hypothesis?

Accepted Answer

$$H_1$$: \mu_d 
eq 0$$

Question 10

Which of the following best describes the degrees of freedom for the paired t-test?

Accepted Answer

$$df = n - 1$$

Question 11

Suppose the mean difference in a paired t-test is negative and the test is left-tailed. If the p-value is less than $$\alpha$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence of a decrease.

Question 12

Which formula is used to calculate the standard deviation of the differences in a paired t-test?

Accepted Answer

$$s_d = \sqrt{\frac{\sum (d_i - \bar{d})^2$}{n-1}}$$

Question 13

A paired t-test is performed at $$\alpha = 0.05$$ and the calculated t-value is in the rejection region. What does this mean?

Accepted Answer

There is enough evidence to reject the null hypothesis.

Question 14

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

Accepted Answer

The population variances must be equal.

Question 15

In a real-world scenario, which of the following would most likely require a paired t-test?

Accepted Answer

Comparing the weights of patients before and after a new exercise program.

Hypothesis Testing with Two Samples: Dependent Samples (Paired Data)

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