UNIVERSITY OF MALAYA
TEST 2 (30 marks – 15%)
ACADEMIC SESSION 2020/2021: Semester 1 SIX1003: Biostatistics
January 2021
INSTRUCTIONS TO CANDIDATES:
Time: 90 minutes
1. Answer ALL questions in this test.
2. Write your answer manually on A4-line paper, scan and submit the scanned file OR
type your answer, save it as PDF, and submit the file. You can also use both writing
and typing in the same document.
3. Underline the answer(s) for each question.
4. NO NEED to copy down the questions on your answer sheet AND
5. NO NEED for the TITLE PAGE (a page with Name, Matrix no., lecturer’s name & UM
logo)
6. SAVE file as ‘Matrix/Registration no._First name’: e.g. 16000001_Normaniza
7. Scan and upload your answer in a single PDF file onto both Spectrum AND on MS
Team.
(This question paper consists of 4 questions on 5 printed pages)
1.
SIX1003
An experiment was conducted on 5 samples of pea plants to observe the effectiveness
of a particular fertilizer on the production of peas. Test the hypothesis that the
production of peas is increased after fertilizer treatment at significance level of 0.01.
You are given that tα=0.01, df = 5 = 3.36, tα=0.005, df = 5 = 4.03, tα=0.01, df = 4 = 3.75, and
tα=0.005, df = 4 = 4.60.
Long bean plants
Yield (g/plant)
Before treatment
After treatment
After – Before
A
40
60
20
B
88
85
-3
C
61
72
11
D
50
56
6
E
88
110
22
SUM
Mean
2.
A medical officer has collected health status data for a sample of 200 patients from a
(8 marks)
rural village. Based on the data below, perform a suitable analysis to determine
whether there is a relationship between gender and health status at a significance
level of 0.05.
Gender
Health Status
Good
Poor
Female
52
43
Male
44
61
(5 marks)
2/5
3. An experiment was performed to determine the effect of four different chemicals on the strength of fabric. Five fabric samples from five different companies were selected, and it is believed that the manufacturing processes in the different companies do affect fabric strength as well. Conduct an appropriate analysis on the data below to determine if there are significant differences in chemical treatment on fabric strength at a significance level of 0.05. Conduct a DMRT posthoc test as well if appropriate.
SIX1003
Strength of fabric samples
Chemical Type
A
B
C
D
Total
1
5.1
5.3
5.3
5.2
20.9
2
5.4
6.0
5.7
4.8
21.9
3
5.3
4.7
5.5
5.0
20.5
4
4.7
4.3
4.7
4.4
18.1
Total
20.5
20.3
21.2
19.4
(12 marks)
3/5
4. A researcher is interested in seeing if species diversity (using Shannon-Weiner Diversity Index) is affected by habitat quality in seagrass beds in Port Dickson. Density of seagrass (gram biomass per m2) is used as a measure of habitat quality. Data collected was presented in the table below:
a) Compute the linear regression equation so that species diversity can be predicted from seagrass density (parameters in 3 decimal points).
b) Calculate the predicted species diversity for the mean seagrass density observed (rounded to closest integer).
c) Is seagrass density significantly correlated with species diversity at a significance level of 1%?
(5 marks)
SIX1003
Species diversity (Y)
Seagrass density (X)
1.26
51.3
1.33
54.6
1.35
58.5
1.23
50.7
1.41
61.1
1.74
68.5
1.39
57.2
1.05
48.1
1.20
49.4
1.49
62.4
Mean = 1.34
Mean = 56.18
4/5
List of formulae
TEST OF DIFFERENCE BETWEEN TWO MEANS
𝑠 2 = ∑𝑑𝑖2−(∑𝑑𝑖)2⁄𝑛 ; 𝑠̅ = 𝑠𝑑𝑖 𝑑𝑖 𝑛−1 𝑑 √𝑛−1
Pooled variance, 𝛿2 = (𝑛1𝑠12+𝑛2𝑠22) 𝑛1+𝑛2−2
𝑠̅ =√(𝛿2 +𝛿2)
LEAST SIGNIFICANT DIFFERENCE (LSD)
Paired test:
Unpaired test:
; 𝑑𝑓 = 𝑛1 + 𝑛2 − 2
𝑑
𝑛1 𝑛2
𝐿𝑆𝐷𝜶 = 𝑡𝜶√(2𝑀𝑆𝒆) [MSe = error mean square, r = no. of replicates] 𝑟
SIMPLE LINEAR REGRESSION AND CORRELATION
𝑏 = ∑ 𝑥𝑦 𝑟 = ∑ 𝑥𝑦
∑𝑥2 22 √(∑𝑥 ∑𝑦 )
̅̅ Where,𝑥=(𝑋 −𝑋); 𝑦=(𝑌 −𝑌)
𝑖𝑖
END
5/5