STAT 516 HW 3 

Please write your answers neatly and clearly!

Also, PLEASE make sure your answers to these questions are
written in the same order as the questions are listed in 
the assignment!!

HAND CALCULATIONS:

Do the following by hand, SHOWING WORK.
(You may use a hand calculator to help with the calculations.)

1.  We will analyze the data in Table 6.29 on pg. 281 of the 
textbook.  The dependent variable (Y) is the tensor strength of
sheet metal and the factor is the supplier of the metal.  The 4 
levels for this factor are simply labeled 1, 2, 3, and 4.

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

(a) Calculate the sums of the strengths for each supplier (the 
Y-i-dot values) and the overall sum of all the strengths (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 
0.05).  Among the different suppliers, is there a significant 
difference in mean tensor strengths?

(e) Calculate the residual corresponding to the second Y value 
listed for supplier 1.

COMPUTER CALCULATIONS:

NOTE: For all hypothesis tests, make sure you clearly state the 
conclusion of the test!!

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.

(a) Use PROC GLM to test whether the mean number of insect deaths 
differs across insectide types.  State the null and alternative 
hypotheses, and give the test statistic and P-value of the test.
(Use alpha = 0.05.)

(b) Use the MEANS statement in PROC GLM to find the sample mean 
number of deaths for each of the four insecticides.  List the four
sample means.

(c) 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.

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

(e) 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 6.38 on page 284 of the textbook.  
These data are also given in the SAS code "engineerdata.txt" on 
the course web page.

(a) Use PROC GLM to test whether the mean number of pushups differs 
significantly across experience levels of the engineers. (Use 
alpha = 0.05, and state the test statistic and P-value for the test.)

(b) In particular, suppose it is suspected that the engineers with 5 
years experience have a different mean pushup ability than those with 
10 or 15 years experience.  Using an ESTIMATE statement, perform a t-test 
to test for a difference between the mean number of pushups for the 
least-experienced level and the mean number of pushups for engineers in 
the next two levels of experience.  Use alpha = 0.05.  State the null 
and alternative hypotheses, and give the test statistic and P-value of 
the test.

(c) Write down the contrast (the linear combination of means) about 
which you are testing in part (b).  Then make up another contrast that 
is orthogonal to the contrast from part (b).  What is an advantage of 
having orthogonal contrasts?

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.  If the statement 
is false, either correct it or explain why it is false.