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KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
INSTITUT DES SCIENCES ET TECHNOLOGIE
Avenue de l'Armée, B.P. 3900 Kigali, Rwanda
INSTITUTE EXAMINATIONS – ACADEMIC YEAR 2013
FACULTY OF SCIENCE
MAIN EXAMINATION
SECOND YEAR CEIT AND APPLIED PHYSICS SEMESTER II
MAT 3222: APPLIED PROBABILITY AND STATISTICS
TIME: 2 HOURS
MAX.MARKS =60
DATE:
,2013
INSTRUCTIONS
1. This paper has SECTION A and B.
2. Questions in SECTION A are compulsory
3. Answer any TWO questions from SECTION B.
4. No written materials allowed in examination room.
5. Write all your answers in the answer booklet provided.
6. Do not forget to write your registration number.
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SECTION A-COMPULSORY QUESTION
QUESTION 1
a. For male and female age the following calculated values are given:For male Age
For female Age
28.29
29.4
91771
97112
25th Percentile
19
20
75th Percentile
35.75
35
100
100
Sample Mean
n
X
i
2
i 1
Sample size
For this sample age,
i.
Calculate sample standard deviation for male and female age. (4 marks)
ii.
Among the two gender which shows higher variation of age. (4 marks)
iii.
Calculate and interpret 95% confidence interval for the true mean age
difference between male and female individuals. (4 marks)
iv.
Calculate Inter Quartile Range for male and female age. (2 marks)
v.
Interpret the given value of 25th percentile for male age. (2 marks)
vi.
Interpret the given value of 75th percentile for female age. (2 marks)
b. What is the application difference between stratified and cluster random sampling
techniques? (4 marks).
c. State the application difference between binomial and Poisson probability
distribution. (3 marks)
d. State the application difference between chi-square and paired t- test. (3 marks)
e. What is the advantage of calculating Skewness and Kurtosis value for a given
numerical data? (2 marks)
2
SECTION B-FROM THIS SECTION CHOOSE ONLY TWO QUESTIONS
QUESTION 2
Assuming weight for the adult population of a given country is normally distributed with
population mean, µ=50 kilogram and population coefficient of variation=4%.
a) Find and interpret the probability that a randomly selected adult individual will have a
weight of exactly 50 kilogram. (2 marks)
b) Find and interpret the probability that a randomly selected adult individual will have a
weight between 46.08 Kilogram and 53.29 Kilogram.(5 marks)
c) For this question, why it is suggested to use normal probability distribution instead of
binomial probability distribution? (3 marks)
d) What is the difference between variable control charts and attribute control charts.
(3 marks)
e)
In hypothesis testing what do we mean by Type I error? (2 marks)
QUESTION 3
The following table presents six students’ number of lecture attending hours per semester
and their performance in “Applied probability and statistics” course.
Student
Lecture attending Hours
Performance (from 100%)
1.
32
75
2.
36
80
3.
28
65
4.
26
65
5.
30
70
6.
30
74
a. By fitting simple linear regression model,
i.
Find and interpret the value of slope in your model? (5 marks)
ii.
What is the test statistics to check the slope in your model is statistically
significant or not? Why? (2 marks)
iii.
Predict a student’s performance in percentage whose lecture attending hours per
semester is 20.(3 marks)
iv.
Calculate and interpret the Pearson correlation coefficient. (5 marks)
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QUESTION 4
To measure equality of population means, the following data were collected from 10
individuals regarding their diastolic blood pressure measurement before and after taking
rest.
Individual Before
After
1.
90
80
2.
85
80
3.
75
75
4.
82
80
5.
95
85
6.
90
85
7.
100
90
8.
96
89
9.
88
85
10.
90
88
a) Write the null and alternative hypothesis to be tested. (2 marks)
b) Calculate appropriate test statistics and make conclusion at 5% level of
significance. (7 marks)
c) Discuss as how sample size (n) affect length of confidence interval. (3 marks)
d) Write your own null and alternative hypothesis that can be tested using chisquare. ( 3 marks)
“GOOD LUCK”
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