Question

A random sample of n = 50 drill bits is used to put holes into a steel doorframe.
The lifetime of a drill bit is measured as the number of holes drilled before the bit
fails. The average lifetime of a drill bit is 12.68 holes with a standard deviation of
6.83 holes. Which formula should be used to determine a 60% confidence interval
for the mean lifetime of the drill bits?

Answer 1

here as we do not know population standard deviation we will use t distribution and

for 60% CI and (n-1=49)df ; critical value of t =0.849

therefore formula for 60$ CI = $\overline{x} \pm t*s/\sqrt{n}$ =12.68 -/+0.849*6.83/sqrt(50)= 11.86 to 13.50