Question

For a biology project, a student wants to research whether the ice at her local coffee shop is clean and free fromimpurities. Her local coffee shop is always really busy and on average they sell about 500 cups a day. She decides totest 15 ice samples from randomly selected coffee drinks. Determine whether her sample is an appropriate randomsample and a good representation of the population.
Option #1: Yes, her sample is an appropriate, random sample. It is a good representation of the population.
Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.
(7 points)
Option #1
Option #2

Answer 1

Option #2.

Why:
- Fifteen samples out of about 500 cups is too small to reliably represent the population. For example, for a 95% confidence interval and the most conservative proportion (p = 0.5) the margin of error with n = 15 is about 25% (1.96·√(0.25/15) ≈ 0.25), which is very large.
- To get a typical 95% CI with a 5% margin of error you’d need on the order of 200+ samples (finite-population correction for N = 500 gives ≈217); even a 10% margin needs ~80–90 samples.
- Sampling only “coffee drinks” can introduce bias: different beverages, times of day, shifts, or locations of ice (machine, storage bin, employee handling) might have different contamination levels. If samples come from the same time or server they aren’t independent.

How to improve:
- Increase sample size to match the desired precision (use a sample-size formula).
- Stratify sampling across times of day, days, drink types, and different ice sources.
- Use sterile sampling technique and test ice itself (and machine/storage) rather than only finished drinks.

Because of the small n and potential biases, the 15-sample plan is not a good representation of the population.