STAT 280 Lab 7: The Dude Returns

Preliminaries

Excel data file is located at: http://www.stat.rice.edu/~hflores/stat280_gmdavis, denoted as stat280L7.xls

Goal for this lab

To understand how to perform probability calculations and (hopefully) make connections with statistical thought using a continuous random variable.

To increase your understanding of conditional probability. You should notice many similarities from the other lab the dude was involved with.

Setup 1 (population known, sample unknown)

So the same dude from last time walks up to you with 30 people following him.  He sneers, "Hey, now I got my entire family with me.  I know its weird that they're divided up evenly between men and women.  Anyway, we got our blood cholesterol level tested by the doc, and well, you see what happened (see data).  What can you tell me about my family?"

Answer the following questions:
1. Plot a histogram of Cholesterol for all 30 individuals, then plot separate histograms of Cholesterol for males and females.  Make "intelligent" observations about overall distribution, differences, and possible outliers.  It might help to compute some descriptive statistics.  Why are these descriptive statistics not prone to sampling error (although they may be prone to error of other forms)?  In other words, explain why these descriptive statistics are NOT estimates, but are known "computable" values.

2. Suppose I blindly choose one of the dude's family members randomly.  Compute the following:
•	P[male], P[cholesterol>200], P[cholesterol>200 | male], P[female | cholesterol < 200].
•	P[male or female | cholesterol > 200], P[male | cholesterol < 50]
•	Would it be possible to compute some of these probabilities using the normal distribution as an approximation?  Explain and/or give and example.

Summarize your findings for the dude.

Setup 2 (population unknown, sample known)

The same dude walks up to you with the same 30 people in tow.  He sneers, "Heya mac.  I lied last time about these people being my family.  Actually, I randomly selected them in Austin, Texas (independently of course).  So what can you tell me about the people in Austin?"

We know think of these people in a different way, as a sample instead of a population.

Answer the following questions:
1. Look back at those histograms you made in Setup 1, question 1 above.  The histograms now describe the shape of the sampling distribution of these people.  Comment specifically on how the observations you made in the first step change meaning.  Are our descriptive statistics now estimates?  If so, of what?  If not, what exactly are they?

2. Assuming that the normal distribution is a reasonable distribution for our data, compute the following:
•	Approximate the percentage of men in Austin with cholesterol over 220.
•	Approximate the percentage of women in Austin with cholesterol lower than 180.
•	Compute a 95% confidence interval for cholesterol in men.  What percentage of men fall in this interval?
•	*Trick Question*: Approximate the percentage of men in Texas with cholesterol over 200 and over the age of 45.

3. Can you argue "statistically" that cholesterol levels are significantly different between men and women?  Explain.

4. What is the sampling distribution of sex?  Compute the proportion of successes (a success being male, failure being female).  Compute the standard deviation.  What do these numbers mean?

Final Report

As last time, none needed.  Just write up your the answers to your questions in an neat, organized fashion.