In: Statistics and Probability
Test runs for the operating time before overeating of 9 randomly selected motors of a certain type showed a sample mean of 39.7 hours and a sample standard deviation of 2.5 hours. Find a 95% confidence interval for the standard deviation of the length of time a motor of this type will operate before overheating.
We have given here,
Sample standard deviation=2.5 hours
Sample size =9
Degree of freedom =n-1= 8
Level of significance given =1-0.95=0.05
Chi square critical value for lower tail=2.18
Chi square critical value for upper tail=17.535
We can use here confidence interval formula for population standard
deviation
=(1.69,4.79)
Lower confidence limit for population standard deviation=1.69
hours
Upper confidence limit for Population standard deviation=4.79
hours