Chapter 10.2, Problem 43E

To determine

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

Answer to Problem 43E

All conditions are met.

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 satisfied because the samples are independent random samples.

Independent: It is satisfied because it is given that the sample are independent and the sample size is less than $10\%$ of the population size.

Normal: It is not satisfied because the sample size of both the samples $50$ is at least $30$ .

Thus, all the conditions are satisfied.