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. The student who weighs his rock 5 times uses the mean to calculate the 95% confidence interval for the rock weight (in grams). His interval is (25.2, 29.1). What does a 95% confidence interval for rock weight tell us in this case

Answer 1

The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.

Explanation:

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.

The confidence interval is given by

`CI = \bar{x} + t_(\alpha/2)((\sigma)/(√(n) ) ) \\`

Where
`\bar{x}` is the mean weight
`\sigma` is the standard deviation
`t_(\alpha/2)` is the critical value from t-table and n is the sample size.

The term
`t_(\alpha/2)((\sigma)/(√(n) ) )` is known as margin of error.

As the sample size is decreased the corresponding margin of error increases which results in wider confidence interval which means smaller precision.

The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.

We can say with 95% confidence that the true mean weight of the rock is within the interval of (25.2, 29.1).