Question

Two studies estimate the mean caffeine content of an energy drink. Each study uses the same test on a random sample of the energy drink. Study 1 uses 25 bottles, and study 2 uses 100 bottles. Which statement is true?

a) The estimate of the actual mean caffeine content from each study will be equally uncertain.
b) The uncertainty in the estimate of the actual mean caffeine content will be larger in study 1 than in study 2.
c) The uncertainty in the estimate of the actual mean caffeine content will be smaller in study 1 than in study 2.
d) None of the above

Answer 1

b) The uncertainty in the estimate of the actual mean caffeine content will be larger in study 1 than in study 2.

Typically, larger sample sizes result in more precise estimates of the population mean. Therefore, study 2 with a sample size of 100 is likely to have less uncertainty in its estimate compared to study 1 with a sample size of 25.