Stat 514        Fall 2010       Test 2       Take Home Questions

Bring these results and your calculations to the exam on November 8.  Keep answers on separate sheets, as you will hand in the solution to one or more problems. 

 Data was collected on the nutritional content of candy bars.  You can use this SAS code to read in the data.

 1. Perform a parametric and a nonparametric test of the equality of the total fat content of candy bars by the company that makes the candy bar.  Are the assumptions of the parametric test met?

2. Calculate Pearson’s correlation, Spearman’s correlation, and Kendall’s tau to examine the relationship of calories and total fat in the candy bars.  Create a plot of the data and test for association using each of the three measures. 

3. A study was conducted to compare prices of boxes of candy bars at four internet candy stores. Here are the results (prices in dollars):

  Store 1 Store 2 Store 3 Store 4
Milky Way 28.95 28.80 36.00 23.79
Milky Way Midnight 24.22 19.75 24.00 17.19
Three Musketeers 32.32 29.80 37.00 22.32
Snickers 37.95 38.40 48.00 36.82
Hershey's 22.99 28.80 36.00 25.90

Based on these data, perform both a parametric and a nonparametric test of the null hypothesis that the price for candy bars  is the same at the four stores. 

4.  The candy bar data include information about whether or not each candy bar contains transfat.   

a. Perform a permutation test of homogeneity of row proportions, to see if the proportion of candy bars containing transfat  differs between companies.

b. Is it appropriate to use the large sample chi-square approximation for the chi-square statistic for these data?

5. Describe a situation when analyzing two variables that the Pearson correlation would be a more appropriate measure of association than Kendall’s tau.  Describe a situation when the reverse is true.