In: Statistics and Probability
A manufacturer of AAA batteries performs quality control checks to verify that they fall within their designed specifications. Battery life is normally distributed, and a sample of 15 batteries yields an average battery life of 142 hours and a standard deviation of 4.8 hours when tested. Create a 95% confidence interval for the population standard deviation of battery life.
Solution:
Given:
Sample size = n = 15
Sample standard deviation = s = 4.8
Confidence level = c = 95%
We have to create a 95% confidence interval for the population standard deviation of battery life.
Formula:
where
and are chi-square critical values for right and left tails.
c = 0.95 , then
Area for right tail critical value:
and Area for left tail critical value:
df = n - 1 = 15 - 1 = 14
Thus we get:
and
Thus we get:
Thus a 95% confidence interval for the population standard deviation of battery life is between 3.51 hours and 7.57 hours.
(Round final answer to specified number of decimal places)