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 Confidence Intervals with an unknown sigma(40pts):

Instead of having a known sigma equal to 8, suppose you simply do not know what the true population standard deviation is. Instead you compute ‘s’, the standard deviation of your sample and find that it equals 10. Based on your data you want make predictions about what the true population mean may be.

1) Given your original sample of 100 students: between what range of values can you be 95% confident that the mean (mu) is? (20 pts)

2) Given your original sample of 100 students: between what range of values can you be 80% confident that the mean (mu) is? (20 pts)

Answer 1