A researcher wishes to construct confidence intervals for a mean with a small random sample (N = 40). What must she assume?
A) The distribution of the population is normal.
B) The distribution of the sample is identical to the distribution of the population.
C) The standard deviation of the population is no bigger than 2× the size of the mean.
D) The size of the population is at least twice the size of the sample.

Question

Quizplus · Accepted Answer

For small sample sizes (N < 30), the population distribution should be normal to use the t-distribution for confidence intervals. However, for N = 40, the sample size is considered large enough for the Central Limit Theorem to apply, but assuming normality of the population is still a common practice for more accurate results.

A Researcher Wishes to Construct Confidence Intervals for a Mean