Third Year Assessed Assignment 2022
University of Dhaka
Department of Statistics
Course Name: ANOVA and Linear Inference
STAT H-308, Credit: 2, Total Mark: 10
Course Instructor: AHS
Problem 1: A textile engineer performs an experiment to investigate which of 4 different carpet
fiber blends produce the best quality carpet. The four different fiber blends considered are
[3]
type 1: nylon fiber blend
type 2: nylon-acrylic fiber blend
type 3: polyester fiber blend
type 4: polypropylene fiber.
Various samples of carpets made with fibers of these four types are subjected to typical amounts
of stress. After a suitable amount of time the worn carpets are taken to be examined by a set of
experts who score the carpets on the amount of wear observed and on the general quality of the
carpets. The scores on each sample of carpet are shown in following table. Higher scores indicate
carpets that are in a better condition.
Type 1
4.98
7.68
3.93
5.91
5.61
8.51
6.02
6.06
5.12
8.33
2.97
5.39
8.97
3.02
Type 2
7.44
8.12
5.44
7.04
9.20
6.34
8.91
8.31
8.44
5.84
10.65
7.63
8.54
7.87
Type 3
6.39
5.31
6.23
7.02
7.02
5.35
3.12
3.12
3.12
6.35
4.70
5.23
4.09
6.02
Type 4
7.51
3.29
3.86
2.91
2.84
3.19
1.68
7.58
5.14
4.12
2.70
1.04
3.60
1.83
(i)
(ii)
(iii)
Analyze the carpet fiber blends data and test the significance of fiber blends at both 5%
level of significance by assuming that these four samples came from four independent
normal population with common variance 𝜎 2 .
Estimate the 𝜎 2
If fiber blends are significantly different in question (i) then determine which pairs are
different using Fisher’s LSD method.
Problem 2: In problem 1, there are equal number of observations in every fiber blend. Suppose
you are told to make a new data layout by considering unequal number of observations under each
fiber blend where type 1, type 2, type 3 and type 4 fibers contain 9, 11, 7, 10 observations,
respectively. You are advised to take a random sample of size 9 from 14 observations of type 1 to
get the observations of type 1 for new data layout. You should follow the same advice to get the
observations for the other three types from the original three types respectively. You are also
advised to use your class roll number as a seed number when you draw a random
sample. Although new data set (unbalanced data) is formed by taking a random sample from the
balanced data set but pretend that this consists four samples which came from four independent
normal population with common variance 𝜎 2 .
[6]
(i)
(ii)
(iii)
(iv)
(v)
Display the new data layout (it is expected that every student should get different
observations under each type)
Analyze the new carpet fiber blends data and test the significance of fiber blends at 5%
level of significance.
If fiber blends are significantly different in question 2. (ii) then determine which pairs
are different.
Find the 95% confidence interval/s for the difference of pairs which are different.
From the results of problems 1 and 2, investigate whether there is any effect of
considering unbalanced data on the significance of fiber blends.
Problem 3: What will be the minimum value of 𝛼 to reject the null hypothesis for the following
ANOVA table? (need to find the 𝑝 value, you are supposed to be taught finding 𝑝 value in Test of
Hypothesis course)
[1]
Source of
Variation
Treatment
Error
Total
D.F.
SS
MS
F
𝑭𝒕𝒂𝒃𝒍𝒆.𝒗𝒂𝒍𝒖𝒆
2
9
11
16.122
0.694
16.81
8.0610
0.0772
104.45
4.26
THE END