Question

The lifetime of an expensive filament is known to be normally distributed, to an excellent approximation, but no other prior information is available. A random sample of 5 filaments has a sample mean lifetime of 968 hours and sample standard deviation of 27 hours. Find a two-sided 95% confidence interval estimate for the true mean lifetime of the filament a

Answer 1

sample std dev ,    s =    27.0000
Sample Size ,   n =    5
Sample Mean,    x̅ =   968.00

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   4          
't value='   tα/2=   2.7764   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   27.000   / √   5   =   12.0748
margin of error , E=t*SE =   2.7764   *   12.075   =   33.525
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    968.00   -   33.525   =   934.475
Interval Upper Limit = x̅ + E =    968.00   -   33.525   =   1001.525
95% confidence interval is (   934.48   < µ <   1001.52   )