Statistics (Lee) Homework 5 Due March 29, 2011

1. Suppose that out of a random sample of 80 BHSEC II students, 17 are left-handed. Studies suggest that roughly 10 percent of the world population are left-handed. Feel free to use R to calculate the probabilities in the questions below. (a) Assuming that event of being left-handed is binomially distributed, what is the probability that 17 out of 80 people sampled are left-handed? (b) What is the one-sided p-value associated with finding 17 out of 80 people who are left-handed? (c) Is finding 17 out of 80 people who are left-handed an unusual statistical event (where statistically unusual means p-value <.05)? 2. Suppose you go on vacation somewhere in the US and the population seems to consist of A LOT of people 65 years of age and over. You are puzzled and you actually take a random sample of 150 people and 30 of the people counted are definitely senior citizens. Based on the US Census Quick Facts resource, 12.9 percent of people in the US are over 65 years old and over. Feel free to use R to calculate the probabilities in the questions below. (a) Assuming that each person counted is an independent event, what is the probability that 30 out of 150 people are 65 years old and over? (b) What is the one-sided p-value associated with finding 30 out of 150 people in the US who are 65 years of age and older? (c) Is finding 30 out of 150 people who are 65 and over an unusual statistical event (where statistically unusual means p < .05)? (d) If the sample size is large enough, we can p approximate a binomial distribution with a normal distribution with mean µ = np and σ = np(1 − p). i. Using this normal approximation, what is the z-score for finding 30 people aged 65 and over? ii. What is the p-value of this z-score? iii. How close is it to the one you found using the binomial distribution? Is it pretty close? 3. Please do the following textbook exercises from Chapter 6 on the Normal distribution: 28,40,41,44,46,49,50 4. R assignment This week you will be looking at data collected by the Centers for Disease Control called the National Health and Nutrition Examination Survey (NHANES) which studies the health and nutrition of adults and children in the US. This study has been going on since the 1960s and we will be looking at the data collected in 2007-2008 on weight and weight loss. I have cleaned the data of major outliers so that trends in the data are more apparent. The data set you will be using is called NHANES.csv. The following are the variables that are included in the data set. Cur.Height Cur.Weight Opinion.of.Weight Like.Change.Wt Ideal.Weight Weight.Last.Yr Diff.Cur.Ideal Change.1yr.Weight Tried.To.Lose.Wt

Current height of subject in inches Current weight of subject in pounds A categorical variable of how the subject feels about his/her weight Would the subject like to change his/her weight? The subject’s ideal weight in pounds The subject’s weight last year in pounds Current weight - Ideal weight Current weight - Last year’s weight Did the subject try to lose weight?

(a) Download the file NHANES.csv by doing the following: 1

i. Go to the course website. Click on “Data” and then click on NHANES.csv. You should see a Google docs spreadsheet. ii. Within the Google doc, click on “File” in the light blue menu bar. Select “Download As” → “CSV (Current Sheet)”. iii. Save the file somewhere under the filename NHANES.csv (b) Import the data into R using the following code which should look familiar. Type your commands into Notepad and then copy and paste into R. setwd("PUT THE LOCATION OF YOUR FILE HERE DON’T FORGET TO USE FORWARD SLASHES") getwd() nhanes=read.table("NHANES.csv", header=T, sep=",") attach(nhanes) (c) Please answer the following questions regarding the variables in the data set. i. What are the numeric/continuous variables in this data set? ii. What are the categorical variables in this data set? iii. How many observations are there in this data set? (d) Find the summary statistics of the numeric/continuous variables. Also, make histograms and boxplots for the numeric/continuous variables? Are the histograms symmetric? Skewed? Do the shapes of the histograms make sense to you? (e) Find associations between Cur.Height and Cur.Weight by plotting them against each other. Do you see any trends? Find the correlation between the two variables (we will do this in lab on Thursday/Friday). (f) Compare the variable Change.1yr.Weight between different groups of the variable Tried.To.Lose.Wt by making boxplots on the same screen. What do you notice? (g) Compare the variable Ideal.Weight between different groups of the variable Opinion.of.Weight by making boxplots on the same screen. What do you notice? (h) For this R assignment, please only turn in a print out of the code you used and the observations that you were asked to make above. We have a functional computer lab on the 6th floor of the school replete with printer; you have no excuse for not turning in this homework assignment with a printout of your code. :-)

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