Question 1

Which of the following is an assumption of the two-sample t-test when comparing two independent groups?

Accepted Answer

Both samples must be random and have normal distributions.

Question 2

A researcher wants to compare the mean horn length of horned lizards killed by shrikes to those that survived. Which statistical test should be used if the data are normally distributed?

Accepted Answer

Two-sample t-test

Question 3

If the data from two independent groups are not normally distributed, which test is most appropriate?

Accepted Answer

Wilcoxon rank sum (Mann-Whitney U) test

Question 4

What does the p-value represent in the context of a two-sample t-test?

Accepted Answer

The probability of observing the data, or something more extreme, if the null hypothesis is true

Question 5

Given the formula for the t-test statistic: $$t = \frac{\bar{y}_A - \bar{y}_B}{SE_{diff}}$$, what does $$SE_{diff}$$ represent?

Accepted Answer

The standard error of the difference between the two means

Question 6

A histogram of horn length for two groups is strongly skewed. Which test should you use to compare the groups?

Accepted Answer

Wilcoxon rank sum (Mann-Whitney U) test

Question 7

Which of the following best describes the null hypothesis ($$H_0) $$for a two-sample t-test comparing mean horn length between two groups?

Accepted Answer

The mean horn length does not differ between the two groups.

Question 8

Why is it important to check the distribution of your data with a histogram before performing a two-sample t-test?

Accepted Answer

To verify the assumption of normality

Question 9

In the horned lizard study, what is the explanatory variable?

Accepted Answer

Condition (killed by shrikes or alive)

Question 10

Which of the following scenarios would require the use of a paired t-test instead of a two-sample t-test?

Accepted Answer

Comparing blood pressure in patients before and after treatment

Question 11

If you perform a two-sample t-test and obtain $$p = 0.0002$$, what is the correct interpretation?

Accepted Answer

There is strong evidence to reject the null hypothesis at $$\alpha = 0.05$$

Question 12

Which test considers medians rather than means and does not require normal distribution?

Accepted Answer

Wilcoxon rank sum (Mann-Whitney U) test

Question 13

A biologist collects horn length data from two groups of lizards: those killed by shrikes and those alive. The data are not normally distributed. Which null hypothesis should be tested using the Mann-Whitney U test?

Accepted Answer

$$H_0$$: The median horn length does not differ between groups.

Question 14

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

Accepted Answer

Both samples are paired

Question 15

What is the main difference between the two-sample t-test and the Mann-Whitney U test?

Accepted Answer

The t-test compares means and assumes normality; the Mann-Whitney U test compares medians and does not assume normality.

Question 16

Which of the following best describes the response variable in the horned lizard study?

Accepted Answer

Horn length

Question 17

A scientist wants to compare the effect of two diets on fish growth. The data are continuous and normally distributed. Which test should be used?

Accepted Answer

Two-sample t-test

Question 18

Which of the following is a correct step when preparing to perform a two-sample t-test?

Accepted Answer

Check the normality of each group using a histogram

Question 19

If the sample sizes of two groups are different, can you still use the two-sample t-test?

Accepted Answer

Yes, as long as the other assumptions are met

Question 20

Which of the following is a real-world example where a two-sample t-test would be appropriate?

Accepted Answer

Comparing the average test scores of students from two different schools

Statistical Comparison of Two Independent Groups: t-Test and Mann-Whitney U Test

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