Question

A study of road rage asked 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 $0-20$. The respondents were chosen by random-digit dialing of telephone numbers. Are the conditions for inference about a difference in means satisfied?

a. Maybe; the data came from independent random samples, but we should examine the data to check for Normality.

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

c. No; a paired $t-$test should be used in this case.

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, and the$10\%$ condition is met.

Short answer

The correct option is (e) Yes; we have two independent random samples and large sample sizes, and the $10\%$condition is met.

Step-by-step solution

Given information

A study of road rage asked random samples of $596$ men and $523$ women about their behavior while driving.

Explanation

We know that we are comparing the sample means of both quantities in the query. The T test does not assume that the populations are normally distributed, but it does assume that the two sample means are.

This assumption is automatically met if the populations are regularly distributed. While this is true, the observations are not normally distributed because the scale is integers from $0-20$and the samples are large enough for the $T$test to provide good inference accuracy.

The $10\%$condition is that our sample size does not include nearly the complete population.

A finite population correction would be employed in this scenario since the number of respondents (just over $1100$) is not close to the population size. As a result, option (e) is the proper choice.