Question

There are​ 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without​ replacement, are the selections independent or​ dependent? If the selections are​ dependent, can they be treated as independent for the purposes of​ calculations? Are the selections independent or​ dependent?

Answer 1

The selections are dependent.

Yes, they can be treated as independent (less than 5% of the population).

Explanation:

Since the selections are made without replacement, each selection affects the outcome of the next selection and, therefore, the selections are dependent.

Although they are dependent, the selections can be treated as independent if the sample size is no more than 5% of the total population. In this case, the sample size is 1235 adults out of a population of 15,958,866 adults. The percentage represented by the sample is:

`P=(12,345)/(15,958.866)*100\\ P=0.077\%`

Thus the selections can be treated as independent for the purposes of calculations.