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 smaller the sample size of marbles, the smaller the sampling variability.
B
The larger the sample size of marbles, the larger 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
Larger samples tend to give sample proportions that are closer to the true proportion in the jar, because random differences average out across more marbles. Sampling variability therefore decreases as sample size increases. Choice D correctly states this; choice B reverses how sample size affects variability.
AI-written and checked against the verified answer.