Make a clear distinction between your population and your sample. A confidence interval can only apply to your sample, it makes no sense when referring to the population parameter.
You know the population mean and standard deviation (in a real application you would not know these under most circumstances) and you have a sample mean (in a real application you would probably also have a sample s.d). Leaves you in the somewhat odd (realistically, but not theoretically) position of using the *population s.d.* to create an interval around a *sample mean*, with an N that is *not* equal to 120, as in your calculations below. -----Original Message----- From: Albert [mailto:[EMAIL PROTECTED] Sent: Thursday, July 10, 2003 10:23 PM To: [EMAIL PROTECTED] Subject: UCL/LCL problem A diet food company has 120 salesman. Monthly sales of each salesman is approximately normally distributed with a mean sales amount of $53,000 and a standard deviation of $15,000. A random sample of 10 salesman is randomly selected. Suppose that the sample mean sales amount turn out to be $63,000, construct a 95% confidence interval for the true mean among the 120 salesman. Solution: I calculated the mean and standard deviation of the sample mean sales to be $53,000 and $4384.67 respectively. bar X = 63000, n = 120, s.d.= 15,000 95% confidence = (1-a) where a = 0.05; hence a/2 = 0.025 ,so Zvalue(.025) = 1.96 = bar X +/- Z(a/2) (sigma/sqroot(n)) = 63,000 +/- (1.96)*15000/sqrt(120) = 63,000 +/- 2,683.8405 LCL = 60316.1595 UCL = 65683.8405 Is the solution correct? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
