Question 1

Which of the following is an assumption that must be checked for BOTH groups when constructing a confidence interval for the difference between two independent means?

Accepted Answer

The data in each group must be nearly normal.

Question 2

A researcher wants to compare the average blood pressure between two independent groups: smokers and non-smokers. Which statistical test should be used?

Accepted Answer

Two-sample t-test

Question 3

Given the following scenario: The mean mass of 29 female turtles is 1397g (SD = 240g), and the mean mass of 20 male turtles is 1548g (SD = 285g). What is the formula for the standard error of the difference in means?

Accepted Answer

$$SE(\bar{y}_1 - \bar{y}_2) = \sqrt{\frac{240^2$}{29} + \frac{285^2$}{20}}$$

Question 4

Which of the following best describes the difference between a paired t-test and a two-sample t-test?

Accepted Answer

A paired t-test analyzes the differences within pairs, while a two-sample t-test compares the means of two independent groups.

Question 5

When conducting a two-sample t-test, which of the following is the correct null hypothesis?

Accepted Answer

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

Question 6

A scientist collects before-and-after measurements on the same plants to test the effect of a fertilizer. Which test should be used?

Accepted Answer

Paired t-test

Question 7

Which of the following is NOT an assumption for the two-sample t-test?

Accepted Answer

The sample sizes must be equal.

Question 8

Suppose you are constructing a 95% confidence interval for the difference in means between two groups. If you estimate the degrees of freedom as $$df = \min(n_1$, n_2$) - 1$$, what is the effect on the confidence interval compared to using the exact formula?

Accepted Answer

The interval will be wider and more conservative.

Question 9

Which formula is used to calculate the test statistic for a one-proportion z-test?

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{SD(\hat{p})}$$

Question 10

A histogram of sample data is strongly skewed to the right. Which of the following is the best course of action before conducting a two-sample t-test?

Accepted Answer

Check if the sample size is large enough (e.g., $$n \geq 20) $$and look for outliers.

Question 11

In a paired t-test, what is the sample size $$n$$ used in the calculation of the test statistic?

Accepted Answer

The number of pairs.

Question 12

Which of the following scenarios would violate the independent groups assumption for a two-sample t-test?

Accepted Answer

Comparing the weights of the same group of turtles before and after a year.

Question 13

Which formula is used to calculate the degrees of freedom for a two-sample t-test using the exact method?

Accepted Answer

$$df = \frac{\left(\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}\$$right)^2$$}{\frac{1}{n_1$-1}\left(\frac{s_1$^2}{n_1$}\$$right)^2$$ + \frac{1}{n_2$-1}\left(\frac{s_2$^2}{n_2$}\$$right)^2$$}$$

Question 14

A 95% confidence interval for the difference in means between two groups is (-5, 15). What does this interval suggest?

Accepted Answer

There is no significant difference between the means at the 5% level.

Question 15

Which of the following is the correct formula for the standard deviation used in the denominator of the one-proportion z-test?

Accepted Answer

$$SD(\hat{p}) = \sqrt{\frac{p_0$ q_0$}{n}}$$

Question 16

A researcher wants to test if the average rent for students has changed after a new housing policy. She collects rent data from the same students before and after the policy. Which test should she use?

Accepted Answer

Paired t-test

Question 17

Which of the following is a correct interpretation of a p-value in the context of a two-sample t-test?

Accepted Answer

The probability of observing a difference as extreme as the one in your sample, assuming the null hypothesis is true.

Question 18

Which of the following is NOT a condition that must be checked before using a paired t-test?

Accepted Answer

The two groups are independent.

Question 19

If the p-value for a two-sample t-test is 0.067 and the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence of a difference.

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

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