Chapter 12, Problem AP4.13CPT

To determine

To find out are the conditions for the inference about a difference in means satisfied.

Answer to Problem AP4.13CPT

Option (e) is the correct option.

Explanation of Solution

In the question, we know that the two quantities we are comparing the sample means of both.The T test does not assume the populations are normally distributed but the two sample means are normally distributed. If the populations were normally distributed then this assumption is automatically met.While it is true, the observations themselves are not normally distributed since the scale are integers from $0-20$ and they are large enough samples for the T test to give high accuracy of inference.

The $10\%$ condition is that are sample size is not taking almost the entire population. In this case, a finite population correction would be used by a little over $1100$ respondents is not close to the population size. Thus, option (e) is the correct option, i.e. Yes, we have two independent random samples and large sample sizes, and the $10\%$ condition is met.