Question

Use this context for the next 4 questions (Questions 1 - 4): Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight. Which student is more likely to come the closest to the true weight of the rock he or she is weighing? (i) The student who weighed the rock 20 times. (ii) The student who weighed the rock 5 times. (iii) Both averages would be equally close to the true weight.

Answer 1

The right answer is:

(i) The student who weighed the rock 20 times.

Explanation:

Both students are taking a sample from the population. In this case, the population is all the possible weight that can be measured by the scale they are using.

Independently of the sample size, the sampling distribution mean will be centered in the population mean, so they are estimating the true weight of the rock unbiased.

But the spread of the sampling distribution, measaured by the standard deviation, depends on the sample size.

The bigger the sample, the narrower the sampling distribution is expected o be. So it is more likely to be closer to the true mean with a bigger sample.

The right answer is:

(i) The student who weighed the rock 20 times.