One common problem with this practice occurs when the samples do not fully reflect the population, or do not reflect the population well. For example, perhaps the population of interest is predominately male, but the sample is predominantly women. This increases the likelihood of the sample producing data that differs from what would be produced by the population. Consider the following research situation:

A group of researchers is studying the relationship between cortisol (stress hormone) levels and memory, and they want to see if a sample of 100 adults that has been recruited is a good representation of the population it came from, before they conduct additional research. The population has been found to be normally distributed and have a mean cortisol level of 12 mcg/dL, with a standard deviation of 2 mcg/dL. The sample was found to have a mean cortisol level of 15 mcg/DL, with a standard deviation of 3 mcg/dL.

For this assignment, construct a confidence interval to determine if this sample mean is significantly different from the population mean. Explain how you know, based on the confidence interval, and specify the confidence level you used. Be sure to show your work and calculations.