In an activity, students are pulling marbles from a large jar containing blue and red marbles. In their sample, students will calculate the proportion of red marbles. Which of the following is a correct statement about sampling variability?
Answer
A
The larger the sample size of marbles, the larger the sampling variability.
B
The smaller the sample size of marbles, the smaller the sampling variability.
C
The larger the sample size of marbles, the closer the sample proportion of red marbles will be to the true proportion of red marbles in the jar.
D
The smaller the sample size of marbles, the closer the sample proportion or red marbles will be to the true proportion of red marbles in the jar.
Explanation
Sampling variability generally decreases as sample size increases. With more marbles in the sample, random differences in the mix of red and blue marbles tend to even out, so the sample proportion of red marbles is more likely to be close to the jar’s true proportion. Therefore, the correct statement is that a larger sample size brings the sample proportion closer to the true proportion.
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