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Chapter 12: Q. AP4.13 (page 829)

A study of road rage asked random samples of 596men and 523women 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 0-20can鈥檛 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 the10% condition is met.

Short Answer

Expert verified

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

01

Given information

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

02

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 0-20and the samples are large enough for the Ttest 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.

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