Which factor influences the width of a confidence interval?

• A. Sample size.
• B. Color of the graph.
• C. Investigator identity.
• D. Time of day data were collected.

Answer: (A)

Confidence interval width reflects how precisely we’re estimating a parameter and is driven by sampling error. Among the options, sample size is the factor that changes this precision. As you collect more data, the standard error (the part that controls the interval’s spread) shrinks roughly in proportion to 1 over the square root of the sample size, so the interval becomes narrower. The color of the graph, who conducted the study, or the time of day the data were collected do not affect sampling variability or the chosen confidence level, so they don’t change the interval’s width.