Question

A decorator is inflating ballons with a helium tank. the ballons can be inflated to their advertised size of 13.5 inches in diameter within three seconds of being hooked up to the tank. however due to uncontrollable factors like the decorator's skill in operating the tank, some of the balloons are largerthen others. randomly selected ballons vary randomly from13.3 inches to 13.7 inches in diameter. To make sure the event is perfect, the decorator wants to estimate the mean balloon diameter to within .025 inches of its true value with a 99% confidence interval. what sample size would he need?

Answer 1

Solution:

We have to first find the estimate of the standard deviation using the range rule of thumb. The estimate of the standard deviation is:

Therefore, the required sample size is:

Where:

is the critical value at the 0.01 significance level.