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? a. the selections are dependent, because the selection is done without replacement. b. the selections are dependent, because the sample size is not small relative to the population. c. the selections are independent, because the sample size is small relative to the population. d. the selections are independent, because the selection is done without replacement. if the selections are dependent, can they be treated as independent for the purposes of calculations? a. yes, because the sample size is less than 5% of the population. b. yes, because the sample size is greater than 5% of the population. c. no, because the sample size is greater than 5% of the population. d. the selections are independent.

Explanation:

1. Selections without replacement are dependent. When one adult is selected, the probability of selecting another changes as the population size decreases.
2. For calculations, dependent selections can be treated as independent if the sample size is less than 5% of the population. Here, the population is 15,958,866 and the sample size is 1235. Calculate $\frac{1235}{15958866}\approx0.000077 < 0.05$.

Answer:

1. A. The selections are dependent, because the selection is done without replacement.
2. A. Yes, because the sample size is less than 5% of the population.