Statistics Math Problem

Question

Suppose you compute a confidence interval with a sample size of 100. What will happen to the confidence interval if the sample size decreases to 50? Explain your answer.

Answer 1

Increasing the sample size always decreases the width of the confidence interval. Conversely, decreasing the sample size increases the width of the confidence interval.

This is because the width is based on the confidence level and the standard error. For a mean, the standard error is

σ /√n

where σ is the standard deviation and n is the sample size.

Since sample size is in the denominator, the ratio increases as the sample size (the denominator) decreases.