Confidence Intervals

An important application of statistics is to estimate population information based on samples. Ideally, we would collect data from entire populations when we wanted to study something, but this is rarely feasible. So instead, we recruit samples (smaller subsets) from populations of interest, with the intent of generalizing the findings.

1. Close Enough?
   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 25 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 have an average cortisol level of 12 mcg/dL, with a standard deviation of 2 mcg/dL. The sample was found to have an average 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 specific the confidence level you used. Be sure to show your work and calculations. This can be tricky with Word, so if necessary, you may take a photo of your hand calculations and add it to the Word document.