Question

A study of road rage asked separate random samples of $596$men and $523$ women

about their behavior while driving. Based on their answers, each respondent was

assigned a road rage score on a scale of $0$ to $20$. Are the conditions for performing a

two-sample t test satisfied?

a. Maybe; we have independent random samples, but we should look at the data to

check Normality.

b. No; road rage scores on a scale from $0$ to $20$ can’t be Normal.

c. No; we don’t know the population standard deviations.

d. Yes; the large sample sizes guarantee that the corresponding population

distributions will be Normal.

e. Yes; we have two independent random samples and large sample sizes.

Short answer

The correct answer is:

e. Yes; we have two independent random samples and large sample sizes.

Step-by-step solution

Given information

We are given separate samples of $596$men and $523$women about their behavior while driving.

Conditions for performing a two-sample t-test: Random, Normal and Independent.

Explanation

Random: I'm satisfied because the samples were supplied to me at random.

Normal: Because each sample has a sample size of at least $30$, it can be presumed to be satisfied.

Independent: Satisfied. Because the random samples were given to be separate, they are now independent. Furthermore, the sample sizes are less than $10\%$of the whole population.

Because all three conditions have been met, answer (e) is correct.