Narrowing a pilot interval

Topic: Estimation examples · more questions on this topic
‹ Household spending on fuel Printer paper ›

A pilot sample of 100 elderly people in nursing homes gave a 95% confidence interval (59.3,\,82.5) kg for the mean weight. What sample size is needed for a 95% margin of error of 1 kg?

Worked answer (click to show)

The pilot half-width is (82.5-59.3)/2=11.6 kg at n=100. The margin scales as 1/\sqrt n, so a margin of 1 kg needs

n\ge 100\times 11.6^2=13456.

Recovering the pilot standard deviation with a t_{99} quantile near 1.98 and then planning the new interval with z_{0.975}=1.96 lowers the requirement to 13188. Either figure is a sample of more than thirteen thousand.