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 $0$to $20$. The respondents were chosen by random digit dialing of telephone numbers. Are the conditions for two-sample t inference satisfied?

(a) Maybe. The data came from independent random samples, but we need to examine the data to check for Normality.

(b) No. Road rage scores in a range between $0$and $20$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

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

Step-by-step solution

Given information

We have been given that,

Number of samples of women =$523$

Number of samples of men = $596$

We need to find whether the conditions for two-sample t inference satisfied.

Simplify.

We know ,

The conditions for performing a two-sample t- test are: Random , Normal , Independent.

Random : This condition is satisfied because the samples have been given to the random samples.

Normal: Can be assumed to be satisfied, because the sample size of each sample is at least $30$.

Independent : Satisfied . The random samples have been given to be separate and thus are independent .Moreover ,the samples sizes are less than $10\%$of the population size.

Thus all the three conditions have been satisfied and thus answer (e) is correct.