A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 1
6 oz. serving size. The sample mean is 13.80 with a sample standard deviation of 1.57. Assume the underlying population is normally distributed. Find the 95% Confidence Interval for the true population mean for the amount of soda served. a. (12.42, 14.18)
Normally, you would find the Confidence interval of a normal sample by using
X(-+) Z* Sigma/n
Where x is the mean, sigma the standard deviation n the size of the sample and z the value determined by your confidence interval size of 95%
.However, this approximation of a confidence interval may only be used for a sample if the number of observations is at least 30 or above. When we have less observations than 30 we must use the standard deviation of the populations. But we only have a sample standard deviation so its not adequate or possible to determine CI the true mean of the population with such a small sample size.
