Assignment 7, Fall 2000

STATISTICS 403 - Assignment 7

Due Thursday, November 9, 2000

M&Ms are packaged in small packages for individual sale in vending machines. Each package has a labeled weight. The actual weight of contents may differ from the labeled weight due to variability in the packaging process or the product being packaged. Below are deviations from the labeled weight (grams) for 15 small bags of Plain M&Ms and 15 small bags of Peanut M&Ms. A positive deviation indicates that the contents of the bag weighed more than the labeled weight. A negative deviation indicates that the contents of the bag weighed less than the labeled weight.
```
            Plain M&Ms                        Peanut M&Ms

     2.6  1.7  0.3  2.0  2.8         1.0   3.9  5.8  -0.1  6.5
     2.6  1.0  1.6  1.5  2.6         2.7   1.9  3.1   0.5  2.1
     1.6  2.1  2.3  3.9  2.5         4.6  -1.3  2.6  -2.1  1.6
```
- Graphically display the data and compare the distributions of the deviations from the labeled weight for Plain and Peanut M&Ms.
- Use the Siegel-Tukey procedure to test to see if the distributions for the two types of M&Ms differ in terms of scale.
- Use the Fligner procedure to test to see if the distributions for the two types of M&Ms differ in terms of scale.
- How do the two procedures compare?
Below are the scores for eleven women golfers for a tournament that consisted of two rounds of golf.
```
Golfer        1    2    3    4    5    6     7    8    9   10   11
--------------------------------------------------------------------
Round 1, X   89   90   87   95   86   81   115   83   88   91   79
Round 2, Y   94   85   89   89   81   76    89   87   91   88   80
--------------------------------------------------------------------
```
- Plot the data. Comment on the apparent relationship between the scores for the two rounds. Are there any unusual points on the graph?
- Calculate the Pearson Product Moment Correlation coefficient, r, for these data.
- Repeat (b) on the 10 golfers excluding golfer #7. How does the value of the Pearson correlation coefficient change?
- Calculate Spearman's Rank Correlation coefficient, r_S, using the scores for all 11 golfers.
- Is the value of r_S based on the 11 golfers statistically significant?
- Repeat (d) on the 10 golfers excluding golfer #7. How does the value of Spearman's correlation coefficient change?
- Is the value of r_S based on the 10 golfers excluding golfer #7 statistically significant?
- The value of r in (b) is not significant (P-value=0.154) but the value of r in (c) is significant (P-value=0.037). What general statement can you make about the affect of extreme points on the Pearson and Spearman correlation coefficients?