1. Do the data below come from an F distribution with  2 (numerator) and 4 (denominator) degrees of freedom? To answer this, do the following:
a) What are the 10th, 20th, 30th, .... 90th percentiles for this F-distribution?  (Hint: Look under ARC: Calculate Probability...)
b) What are the 10th, 20th, 30th,...9th percentiles for the data below?  (Note: the 10th percentile has roughly 10 percent of the observations below it.  And about the same number of observations need to be between each 10th-percentile (Another Note: these are called deciles, sometimes.))
c) Either by hand or by the computer, plot the F-distribution deciles on the x axis, the sample deciles on the y axis.
d) If the sample really did come from an F(2,4) distribution, what should you see?
e) Do you think this sample came from the F(2,4) distribution?

Data (for your convenience, the data have been sorted.)  n = 20
0.03,  0.05,  0.08,  0.12, 0.28,  0.38,  0.48,  0.50,  0.52,  0.67, 1.07,  1.77,  1.01, 1.16, 1.57, 1.67, 1.72,  2.39, 3.5, 14.34

Helpful Arc Hint:  If you want to type data by hand into ARC, see the ARC Hints

2.  Does storing bread lower the amount of vitamin E in the bread?  Five loaves were baked.  Two had the amount of vitamin E measured immediately after baking (in mg/100g of flour).  Two others were stored for three days and then the vitamin E was measured. Here are the data:

Immediately after baking: 94.6, 96.0, 95.0
3 days after baking: 97.4 94.3

Is this evidence that the amount of vitamin E has decreased?  Do a non-parametric test based on ranks:
a) State the null and alternative hypotheses.
b) Let R be the sum of the ranks of the "3-days after baking" group.  What is the observed-R?
c) Under the null hypothesis, give the probability distribution of R.
d) Make a graph of this probability distribution of R and show where observed-R is.
e) What is the p-value?
f) What is your conclusion?

3. In a study of cereal leaf beetle damage on oats, researchers measured the number of beetle larvae per stem in small plots of oats after randomly applying one of two treatments: no pesticide or Malathion at the rate of 0.25 pound per acre.  Is there significant evidence at the 5% level that Malathion is effective?
Control:  2, 4, 3, 4, 2, 3,3, 5, 3, 2, 6, 3, 4
Treatment: 0,1,1,2,1,2,1,1,2,1,1,1
(From Moore and McCabe: Introduction to the Practice of Statistics, 3rd Ed. Data from M.C. Wilson et al., "Impact of cereal leaf beetle larvae on yields of oats," Journal of Economic Entomology, 62 (1969), pp. 699-702))

a) Why would the assumption of normality not apply here?
b) Just for fun, pool the data together and use ARC to make a normal probability plot.   According to the plot, do the data look normal?
c) Examine side-by-side boxplots.  What do they suggest?
d) Perform a sum-rank test at the 5% level.  State your null and alternative hypotheses, and carefully carry out all steps.

4.  Make a 3-d spin plot in ARC:  Using the class data, put height, weight, and TV into the plot.  Spin it around.  Describe the plot of height vs. TV, weight vs. TV, and height vs. weight.  (Spin the plot until you can see these perspectives.) (Use the Graph&Fit: Plot of..  feature. Doesn't matter which variable you put on which axis.)