Chapter 10.2, Problem 44E

To determine

To check if the conditions for calculating a confidence interval for $\text{}\frac{305}{1526}=0.20=20\%{\overline{x}}_{MJ}-{\overline{x}}_{AM}$ are met.

Answer to Problem 44E

Random condition is not satisfied.

Explanation of Solution

We have to check if the conditions are met or not. Therefore,

There are three conditions to be satisfied:

Random: It is not satisfied because the samples are not independent random samples as we conveniently select the first $400$ words and the first $100$ words of the two article.

Independent: It is satisfied because the $400$ words is less than $10\%$ of the population of all words in the medical journal and the sample of $100$ words is less than $10\%$ of the population of all words in the airline magazine.

Normal: It is satisfied because the two samples are large and since $100\text{ is at least 30}$ and $400\text{ is at least 30}$ .

Thus, all the conditions are not satisfied since random condition is not satisfied and it is not appropriate to determine a confidence interval for the mean difference.