STAT 516 HW 3

HAND CALCULATIONS:

1.  We will analyze the data in Table 6.25 on pg. 293 of the textbook (also shown below).  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.

DATA from Table 6.25 of book:

Times to complete maze for three groups of five mice each:
Red:  9, 11, 10, 9, 15
Green: 20, 21, 23, 17, 30
Black: 6, 5, 8, 14, 7

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

(a) Calculate the sums of times for each door color (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 first mouse listed for the Red door.

COMPUTER CALCULATIONS:

2.  Look at the data in Table 6.31 on page 296 of the textbook.  These data and code to read them into R 
are also given in the R code at the link "Insecticide Data Set" on the course web page. The factor is called
'insecticide' and the response variable is called 'dead'.

(a) Use R to test whether the mean number of insect deaths differs across insecticide 
types.  Use alpha= 0.05, and justify your answer by referring to either a test statistic value 
and table value, or by referring to a P-value.

(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 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 given in the R code at the link "Bank Data Set" on the course web page.
The factor, called 'branch', indicates the particular branch office of a bank.  A random sample of 
employees was taken from each branch, and the response, called 'leave', is the amount of sick leave (in days)
taken by the employee.

(a) Use R to test whether the mean number of days of sick leave differs across 
bank branches.  Use alpha=0.05, and justify your answer by referring to either a test statistic value 
and table value, or by referring to a P-value.

(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.  Using a contrast, 
perform a t-test 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.  Use alpha = 0.05.
Write the specific form of the contrast that you are using to answer the research question.

TRUE-FALSE QUESTIONS:

4.  Answer True/False Concept Questions 2, 7, 9, 10,
11, 12(all parts), 13, 15 on pages 288-289.  If the statement 
is false, either correct it or explain why it is false.