Question 1

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

Accepted Answer

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

Question 2

Which assumption is required for the pooled t-test but not for the non-pooled t-test?

Accepted Answer

The population variances are equal.

Question 3

Given two independent samples with sample means $$\bar{x}_1 = 50$$, $$\bar{x}_2 = 45$$, pooled standard deviation $$s_p = 5$$, and both sample sizes $$n_1$$ = $$n_2 = 20$, what is the value of the pooled t-statistic for testing H_0$: \mu_1$ = \mu_2$?

Accepted Answer

$$t = \dfrac{50 - 45}{5 \sqrt{\dfrac{1}{20} + \dfrac{1}{20}}} = 3.16$$

Question 4

A researcher wants to compare the mean cholesterol levels between two independent groups, but suspects the variances are not equal. Which test should be used?

Accepted Answer

Non-pooled t-test

Question 5

Which formula correctly represents the test statistic for the paired t-test?

Accepted Answer

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

Question 6

In a non-pooled t-test, which formula is used to estimate the standard error of the difference in means?

Accepted Answer

$$\sqrt{\dfrac{s_1$^2}{n_1$} + \dfrac{s_2$^2}{n_2$}}$$

Question 7

A clinical trial measures the effect of a new drug by recording patient blood pressure before and after treatment. Which hypothesis test is most appropriate?

Accepted Answer

Paired t-test

Question 8

Which of the following is NOT an assumption of the pooled t-test?

Accepted Answer

The two samples are paired.

Question 9

Suppose you have two independent samples with $$n_1 = 15$, n_2$ = 18$$, $$s_1^2 = 20$, and s_2$^2 = 40. $$Which test should you use to compare the means?

Accepted Answer

Non-pooled t-test

Question 10

Which of the following best describes the null hypothesis for a two-sample t-test?

Accepted Answer

$$H_0$$: \$$mu_1$$ - \$$mu_2 = 0$

Question 11

A paired t-test is most appropriate when:

Accepted Answer

Each observation in one sample can be uniquely matched to an observation in the other sample.

Question 12

Which formula is used to calculate the pooled variance $$s_p^2$ in a pooled t-test?

Accepted Answer

$$s_p^2$ = \dfrac{(n_1$ - 1)s_1$^2 + (n_2$ - 1)s_2$^2}{n_1$ + n_2$ - 2}$$

Question 13

A researcher collects data on the weights of 10 individuals before and after a diet program. The differences are approximately normal. Which test should be used to determine if the diet program is effective?

Accepted Answer

Paired t-test

Question 14

Which of the following is a key difference between the pooled and non-pooled t-tests?

Accepted Answer

The pooled t-test assumes equal population variances, while the non-pooled t-test does not.

Question 15

If the sample variances are very different and the sample sizes are unequal, which test is most appropriate for comparing two means?

Accepted Answer

Non-pooled t-test

Question 16

Which of the following is the correct formula for the degrees of freedom in a pooled t-test?

Accepted Answer

$$df = n_1$ + n_2$ - 2$$

Question 17

A study compares the mean reaction times of drivers before and after drinking coffee. Which test should be used?

Accepted Answer

Paired t-test

Question 18

Which of the following is NOT a situation where a paired t-test is appropriate?

Accepted Answer

Comparing the mean scores of two different classes on a final exam.

Question 19

Which test statistic formula is used for the non-pooled t-test?

Accepted Answer

$$t = \dfrac{\bar{x}_1 - \bar{x}_2}{\sqrt{\dfrac{s_1$^2}{n_1$} + \dfrac{s_2$^2}{n_2$}}}$$

Question 20

A scientist wants to test if two fertilizers result in different mean crop yields. She randomly assigns one fertilizer to one group of fields and the other fertilizer to a different group. Which test should she use?

Accepted Answer

Non-pooled t-test

Hypothesis Tests for Two Population Means: Pooled, Non-Pooled, and Paired t-Tests

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