Question

Suppose you are interested in finding out how happy the students are at UNR. You design a survey that probes aspects of an individual’s emotional life, and using this survey are able to compute an accuracy index score ranging from 0 (completely miserable) to 100 (nauseatingly happy). You know that the standard deviation of the population (sigma) equals 8; however you do not know, and want to know, what the mean of the population (mu) is. Rather than give the survey to every student who attend UNR and calculate mu, you give the survey to a random sampling of 100 students. You collect the accuracy indices and compute the mean of your 100 samples and find the mean (x-bar) = 80. Using the Central Limit Theorem (20pts):

1) Based on the central limit theorem, what is the distribution that your sample mean is drawn from? (10 pts)

2) What would the distribution be if instead of 100 individuals, you sampled 25? (5 pts)

3) If you sampled 25 instead of 100 students, would your sample mean (x- bar) be more or less likely to be close to mu? (5pts)

Answer 1