STAT 516 HW 4B, Fall 2026 


COMPUTER CALCULATIONS:

1.  A study was done to measure the gas requirements for cooking a 
roast to 160 degrees under several conditions.  The factors are Oven 
Setup (levels:  "Preheated" or "Not Preheated") and Meat Condition 
(levels:  "Fresh", "Frozen", "12-hour Thawed", and "24-hour Thawed").  
There were 5 observations assigned to each combination of factor levels.  
The data and R code to read it in are given on the course web page as "roastdataR.txt".

Using R, answer the following questions:

(a) At a 5% significance level, test whether we can conclude that 
there is a significant difference in mean gas usage across cells.
(Give the test statistic value and P-value for this test.)

(b) At a 5% significance level, test whether there is a significant 
interaction between Oven Setup and Meat Condition.  If so, interpret 
what this result is saying.  (Give the test statistic value and 
P-value for this test.)

(c) Create an interaction plot (specifically, plot gas against meat 
condition, for each type of oven setup) and state what this tell you 
about the joint effect of Oven Setup and Meat Condition on gas usage.
Provide your interaction plot with your submitted homework.

(d) At a 5% significance level, is there a significant difference in 
mean gas usage between preheated and non-preheated ovens, when the meat 
is thawed for 24 hours?  Use a contrast to answer this 
question -- be careful to set it up correctly!  (Give the test statistic 
value and P-value for this test.)

(e) At a 5% significance level, is there a significant difference in 
mean gas usage between fresh meat and all non-fresh meat, when the oven 
is preheated? Use a contrast to answer this question -- be 
careful to set it up correctly!  (Give the test statistic value and 
P-value for this test.)

(f) Consider Tukey's procedure for checking for significant differences 
between each pair of factor levels.  At the 5% level, two combinations 
have a significantly different mean gas usage if their sample means differ 
by more than what value? (Hint: the critical value from the studentized range Table A.6 (also on the course webpage) in this 
case is q_.05(t=8,df=32).)

2.  Montgomery gathered data on an experiment in paper production to determine the effects of
pulp cooking time (having two levels: 3 hours and 4 hours), 
vat pressure (having three levels:  400, 500, and 650), and
percent of hardwood concentration (having three levels: 2, 4, and 8) 
on the response variable: paper strength.
The data and R code to read them in are given on the course web page as "paperdataR.txt".

(a) Fit a three-way ANOVA, including ALL possible interaction terms.  
At a 5% significance level, is there a significant three-way interaction?
At a 5% significance level for each test, which of the two-way interactions are significant, if any?
(Give the test statistic values and P-values for the relevant tests.)

(b) Based on your answers to part (a), which of the three tests for MAIN effects is appropriate to examine here?
In other words, for which factor should we test about the main effects of that factor?  Explain.