Question

A manufacturer of pharmaceutical products analyzes a specimen from each batch of a product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise, but the company wants to know the true mean concentration. The laboratory analyzes each specimen 40 times and reports the sample mean concentration to be 0.8404 and the sample standard deviation to be 0.0420.

1. Identify the parameter of interest.

2. What procedure should we use to construct this interval? Z-interval or T-interval

3. Using the interval from question 2, determine the appropriate 95% CI.

Answer 1

1 ) The parameter of interest is , population mean of the concentration of the active ingredient .

2 ) A Z interval can only be used provided the value of the population standard deviation is known . Since , the value of the population standard deviation is not known , hence we cannot use the Z interval . Instead , we have to use a T interval .

3 ) The 95 % confidence intertval of the population mean is given by :

where ,

Required confidence interval :