Jaimie Kwon Page 13 11/23/2004
Stat {4601, 6872} Quiz #2 (50 minutes)
• Open book and open note.
• Use a simple calculator if necessary.
• Show your work. (E.g. Next to each numerical answer, you need to put things like P0.01(B≥3) or
something equivalent)
• All problems are 10 points unless otherwise noted.
1. (100 points) An experiment was conducted to measure and compare the effectiveness of various feed
supplements on the growth rate of chickens. Newly hatched chicks were randomly allocated into three
groups of size 5, 2, and 5, and each group was given a different feed supplement. Their weights in grams
after six weeks are given along with feed types. The data is as follows:
Weight feed
1 179 horsebean
2 160 horsebean
3 136 horsebean
4 227 horsebean
5 217 horsebean
11 309 linseed
12 229 linseed
23 243 soybean
24 230 soybean
25 248 soybean
26 327 soybean
27 329 soybean
28 250 soybean
Answer the following.
a. What’s the relevant nonparametric test?
b. Define the model formally/mathematically (using Xi, Yi, µ, ∆ etc) and state the necessary
assumptions to apply the nonparametric test in a)
c. Formally state the hypothesis (e.g. H0: µ=0 vs. H1: µ >0 where µ is the median …)
d. Compute the test statistic (20pt).
e. Suppose, for the independent data with the same dimension, the test statistic is computed to be
5.0. Can you reject the null hypothesis at 5% significance level? Answer using the corresponding
table in the textbook.
f. Compute the P-value for the test statistic in (e).
g. What’s the equivalent parametric test? What’s the extra assumption(s) you need to make about
the distribution? (be specific)
h. If the parametric and nonparametric tests give different answers, with a very small P-value (say
0.001) for the parametric test and a very large P-value (say 0.20) for the nonparametric test,
what could be possible explanations of the reasons why? In such case, what would you do to clarify
the issue? Finally, which test result would you choose? (20pt)
