In a sample of 50 microdrills drilling a lowcarbon alloy ste

In a sample of 50 microdrills drilling a low-carbon alloy steel, the average lifetime (expressed as the number of holes drilled before failure) was 12.68 with a standard deviation of 6.83. Find an 80% confidence interval for the mean lifetime of microdrills under these conditions.

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=12.68
Standard deviation( sd )=6.83
Sample Size(n)=50
Confidence Interval = [ 12.68 ± t a/2 ( 6.83/ Sqrt ( 50) ) ]
= [ 12.68 - 1.299 * (0.966) , 12.68 + 1.299 * (0.966) ]
= [ 11.425,13.935 ]