Questions: 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 independent, because the sample size is small relative to the population. B. The selections are dependent, because the selection is done without replacement. C. The selections are independent, because the selection is done without replacement. D. The selections are dependent, because the sample size is not small relative to the population.

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 independent, because the sample size is small relative to the population. B. The selections are dependent, because the selection is done without replacement. C. The selections are independent, because the selection is done without replacement. D. The selections are dependent, because the sample size is not small relative to the population.
Transcript text: 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 independent, because the sample size is small relative to the population. B. The selections are dependent, because the selection is done without replacement. C. The selections are independent, because the selection is done without replacement. D. The selections are dependent, because the sample size is not small relative to the population.
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Solution

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Solution Steps

Step 1: Determine Dependence or Independence

Since the selection is done without replacement, the selections are dependent. This means that the outcome of one selection can affect the outcome of subsequent selections.

Step 2: Assessing Independence for Calculations

To assess whether the selections can be treated as independent for the purposes of calculations, we calculate the percentage of the population that the sample represents: $\frac{n}{N} \times 100 = \frac{1235}{15958866} \times 100 = 0.01\%$. Since 0.01% < 5%, the selections can be treated as independent for the purposes of calculations. This is because the impact of not replacing elements is negligible on the probability of subsequent selections.

Final Answer: The selections can be treated as independent for the purposes of calculations.

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