STAT 516 HW 5

Please write your answers neatly and clearly!

You MUST make sure your answers to these questions are
written in the same order as the questions are listed in 
the assignment.  If this instruction is not followed, 
your homework WILL NOT be graded.

HAND CALCULATIONS:

1.  We will analyze the data in Table 6.28 on pg. 281 of the textbook.  
The dependent variable (Y) is the time needed for the mouse to complete 
the maze and the factor is the color of the maze door.  The 3 levels for 
this factor are red, green, and black.

Do the following by hand, SHOWING WORK.  You may use SAS to check your 
answers if you want.

(a) Calculate the sums of times for each door (the Y-i-dot values) and the 
overall sum of all the times (the Y-dot-dot value).

(b) Use your answers from part (a) to find the SSB, SSW, and then the MSB 
and MSW.

(c) Calculate the F ratio and write the complete ANOVA table for this problem.

(d) Perform the ANOVA F-test by comparing the F ratio to the appropriate value 
from the F table (use a significance level of .05).  Among the different door 
colors, is there a significant difference in mean time needed to complete the 
maze?

(e) Calculate the residual for the second mouse listed for the Red door.

COMPUTER CALCULATIONS:

2.  Look at the data in Table 6.34 on page 283 of the textbook.  These data are 
also given in the SAS code "insectdata.txt" on the course web page.
(Similar code to read the data into R is given as well.)

(a) Use PROC GLM to test whether the mean number of insect deaths differs across 
insectide 
types.

(b) For the analysis in part (a), use Levene's test (alpha = 0.05) to check the 
equal-variances assumption.  Also, perform a residual plot and a Q-Q plot of the 
residuals to check for violations in the assumptions.  Summarize your findings.

(c) If the residual plot shows any outlier(s), which data value is responsible?

(d) Perform's Tukey's multiple comparison procedure (using alpha = 0.05) and 
summarize which insecticides are significantly different from each other, in 
terms of mean number of deaths.

3.  Look at the data in Table 6.39 on page 285 of the textbook.  These data are 
also given in the SAS code "bankdata.txt" on the course web page.
(Similar code to read the data into R is given as well.)

(a) Use PROC GLM to test whether the mean number of days of sick leave differs 
across bank branches.

(b) In particular, suppose the bank manager suspects the employees at branches 
1 and 3 have a different mean sick-leave count than those at branch 2.  Write the 
form of the contrast that can be used to test for a difference between the mean 
number of sick days for the first and third branches and the mean number of sick 
days for branch 2.  Also write the null and alternative hypotheses for this test.

(c) The SAS output for this hypothesis test is given on the course web page in the 
file "bankdataoutput.txt".  What are your conclusions about the bank manager's suspicion?  
Use alpha = 0.05.  Give the test statistic value and P-value of the test to justify 
your answer.


TRUE-FALSE QUESTIONS:

4.  Answer True/False Concept Questions 2,4,6,7,9,10,11,12(all parts),13,15 
on pages 279-280.