Description
1. An experiment investigated the effects of different bleaching chemicals on pulp brightness. Three
chemicals were selected at random from a large population of potential bleaching chemicals.
Summary statistics on pulp brightness are given below:
Bleaching Chemical Sample Size Sample Mean Sample SD
1 6 72.843 8.607
2 6 83.386 5.146
3 5 77.257 5.460
An ANOVA table for analyzing the data is given below:
Source DF SS MS F P-value
Chemical 2 336.0 168.02 3.781 0.0486
Error 14 622.1 44.44
Total 16 958.1
Refer to formula set 10K for all the problems below.
a. Briefly explain why a random-effects model is appropriate here.
b. Carry out the hypothesis test based on the ANOVA table at the πΌ = 0.10 level of significance. Show
all 4 steps in hypothesis testing that we follow in class. Use the P-value provided above.
c. Estimate ππ΄
2
the variability due to bleaching chemicals. Show some calculations.
d. What is an estimate of total variance in a single pulp brightness value?
e. What proportion of total variation in a single pulp brightness value is attributed to differences
among bleaching chemicals?
2. Chapter 11: Section 11.1, Exercise 4. βIn an experiment to see whether the
amount of coverage of light-blue β¦β
This is the two-way additive ANOVA table:
Df Sum Sq Mean Sq F value P-Value
A=Roller Brand 2 38.00 19.00 2.803 0.1381
B=Paint Brand 3 159.58 53.19 7.848 0.0169
Residuals 6 40.67 6.78
Total 11 238.25
a. An interaction plot of the data is given on the right. For the
two-way additive model and ANOVA analysis above to be valid,
the plot should show (roughly) parallel curves. Discuss what the
plot tells you.
b. Show by hand calculations that SSA=SS(Roller Brand)=38.00.
c. State and test hypotheses appropriate for deciding whether paint brand has any
effect on coverage. Complete the 4-step procedure we follow in class. Use the given
P-value in the ANOVA table.
d. Repeat part (b) for brand of roller. Use the given P-value in the ANOVA table..
e. Comment on each plot of residuals below.
3. Chapter 11: Section 11.1, Exercise 6. House assessor.
For part (a), follow the 4-step procedure we do in class.
