Question

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. Suppose the students construct a 95% confidence interval for the true weight of their rocks. Whose interval do you expect to be more precise (narrower)

Answer 1

The first student, with 20 measurements, will have the more precise interval due to the larger sample size.

Explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

`M = z(s)/(√(n))`

In which z is related to the confidence level, s to the standard deviation and n to the sample size.

The margin of error is inversely proportional to the square root of the sample size, which means that a larger sample will lead to a lower margin of error, that is, to a more precise interval.

In this question:

One student will use 5 measurements, other 20. The first student, with 20 measurements, will have the more precise interval due to the larger sample size.