Question

Suppose you are trying to estimate the population mean for your company’s production. You have sampled 49 months and you calculated the average production (sample mean), in dollars, to be $900,000,with a standard deviation of $57,000. Note that this standard deviation is of raw data. Your company has population monthly production data for 950 months (quite a long time). Please calculate a confidence interval for your sample mean, assuming you wish to be 96% confident.

Answer 1

Level of Significance ,    α =    0.04  
degree of freedom=   DF=n-1=   48  
't value='   tα/2=   2.111   [Excel formula =t.inv(α/2,df) ]

standard error , SE = s/√n * √((N-n)/(N-1)) =   7934.2541

margin of error , E=t*SE =   2.111*7934.2541=   16749.7929      
              
confidence interval is               
Interval Lower Limit = x̅ - E =    900000-16749.7929=   883250.2071      
Interval Upper Limit = x̅ + E =    900000+16749.7929=   916749.7929      
96% Confidence interval is   883250.21   < µ <   916749.79   )