Question

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)? (i) The student who weighed the rock 20 times. (ii) The student who weighed the rock 5 times. (iii) Both intervals would be equally precise.

Answer 1

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

Explanation:

The margin of error of a confidence interval is:

`M = z*(\sigma)/(√(n))`

In which z is related to the confidence level,
`\sigma` is the standard deviation of the population and n is the size of the sample.

From the equation above, the larger the size of the sample, the lower the margin is, that is, the narrower the interval is.

In this question:

A student weighed the rock 20 times and other the 5. From above, the one who weighed the rock 20 times will have the more precise interval.

So the correct answer is:

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