Question 1

A researcher wants to compare the average test scores of students from two different universities. Which statistical test is most appropriate if the samples are independent and the data are approximately normal?

Accepted Answer

Two-sample t-test

Question 2

Which of the following is NOT an assumption required for constructing a confidence interval for the difference between two independent means?

Accepted Answer

The two groups are paired

Question 3

Given two independent samples with means $$\bar{x}_1 = 50$$, $$\bar{x}_2 = 45$$, standard deviations $$s_1 = 10$, s_2$ = 8$$, and sample sizes $$n_1 = 40$, n_2$ = 35$$, what is the standard error for the difference in means?

Accepted Answer

$$SE = \sqrt{\frac{10^2$}{40} + \frac{8^2$}{35}}$$

Question 4

A wildlife biologist measures the mass of 29 female turtles (mean = 1397g, SD = 240g) and 25 male turtles (mean = 1548g, SD = 285g). What is the null hypothesis for testing if there is a difference in average mass between males and females?

Accepted Answer

$$H_0$$: \mu_{male} - \mu_{female} = 0$$

Question 5

Which of the following scenarios requires a paired t-test rather than a two-sample t-test?

Accepted Answer

Comparing blood pressure before and after treatment in the same patients

Question 6

If the histogram of the differences between paired observations is highly skewed with several outliers, which assumption for the paired t-test is violated?

Accepted Answer

Normality of the differences

Question 7

A confidence interval for the difference in means between two independent groups is calculated as $$CI = (\bar{x}_1 - \bar{x}_2) \pm t^* 	imes SE. $$What does $$t^*$$ represent?

Accepted Answer

The critical value from the t-distribution for the desired confidence level

Question 8

In a two-sample t-test, which of the following would be a reason to subtract the P-value from 1?

Accepted Answer

When the test is one-tailed and the observed difference is in the opposite direction of the alternative hypothesis

Question 9

Which of the following is a correct interpretation of a 95% confidence interval for the difference in means between two groups?

Accepted Answer

We are 95% confident that the true difference in population means lies within the interval

Question 10

A study compares the mean weights of two independent groups. The 95% confidence interval for the difference in means is $$(-2.5, 5.0). $$What can be concluded at the 0.05 significance level?

Accepted Answer

There is not enough evidence to conclude a significant difference in means

Question 11

Which formula correctly gives the test statistic for a two-sample t-test for independent means?

Accepted Answer

$$t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1$ - \mu_2$)}{SE}$$

Question 12

A paired t-test is most similar in calculation to which of the following?

Accepted Answer

A one-sample t-test on the differences

Question 13

Which of the following is a violation of the independence assumption for a two-sample t-test?

Accepted Answer

Measuring the same individuals before and after a treatment

Question 14

Suppose you are testing $$H_0$$: \$$mu_1$$ - \$$mu_2 = 0$ versus H_A$$: \$$mu_1$$ - \$$mu_2$$ \u003e 0$$. The calculated t-statistic is negative. What should you do to find the correct P-value?

Accepted Answer

Subtract the calculated P-value from 1

Question 15

A medical researcher collects cholesterol levels from 30 patients before and after a new diet. Which test should be used to determine if the diet had a significant effect?

Accepted Answer

Paired t-test

Question 16

Which of the following best describes the standard error for the difference in means for two independent samples?

Accepted Answer

$$SE = \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 17

A study finds a 95% confidence interval for the mean difference in blood pressure (after - before) as $$(-1.2, 3.8). $$What does this suggest about the effect of the treatment?

Accepted Answer

There is not strong evidence that the treatment changed blood pressure

Question 18

Which of the following is NOT a condition for using a two-sample t-test for independent means?

Accepted Answer

The two samples are paired

Question 19

If you have two independent samples and want to test if their means are equal, which is the correct null hypothesis?

Accepted Answer

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

Question 20

A paired t-test is used when:

Accepted Answer

The same subjects are measured twice under different conditions

Statistical Inference: Comparing Two Means (Independent and Paired Samples)

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