MAASAI
MARA
UNIVERSITY
REGULAR UNIVERSITY EXAMINATIONS
2015/2016 ACADEMIC YEAR
FIRST YEAR SECOND SEMESTER
SCHOOL OF BUSINESS & ECONOMICS
COMMON COURSE
COURSE CODE: IRD 104
COURSE TITLE: QUANTITATIVE SKILLS II
DATE: 6TH MAY, 2016
TIME: 2.30 – 4.30PM
INSTRUCTIONS TO CANDIDATES
1. Answer Question ONE and any other THREE questions
2. Mobile phones are not allowed in the exam room
3. No writing on the question paper
This paper consists of 2 printed pages. Please turn over.
a) Briefly explain the meaning of the following terms
i.
Regression analysis and correlation
ii. Discrete random variable and continuous random variable
iii. Alternative hypothesis and null
iv.
Point estimate and interval estimate
v. Skewness and kurtosis
(5marks)
b) It is known that from a lot of 100 computers there are 20 defective ones. 5 of these
computers are selected at random and tested. Find the probability that only 2 of the 5 are
defective
(3marks)
c) On the basis of the results obtained from a random sample of 100 men from Narok
County the 95 % confidence interval for the mean height of the men in the district is
found to be (177.22cm,179.18cm)
i.
Find the value of 𝑋̅ , the mean of the sample and 𝝳 the standard deviation of the
normal population from which the sample is drawn.
(3 marks)
ii.
Construct/calculate the 98% confidence interval for the mean height (2 marks)
d) A random sample of 12 items taken from a normal population gave the following data
𝑋̅ = 82, ∑ 𝑋 2 = 686,800
Find the 95% confidence intervals for the population mean.
(2 marks)
e) In a competitive examination of 5000 students, the marks of the examinees in statistics
were found to be distributed normally with mean 45 and standard deviation 14.
Determine the number of examinees whose marks out of 100 were
i.
Less than 30
(1 mark)
ii.
Between 30 and 70
(2 marks)
iii. More than 40
(1 mark)
f) The demand and price (in Ksh ‘000’) for a bag of a hybrid 100kg bag of wheat in
different regions of the country is as shown below
Price (in Ksh
7
9
8
11 13 12
‘000’)
Demand
24 28
25 30 31 30
Calculate the Pearson correlation coefficient and comment on your answer.
(6marks)
QUESTION TWO (15 MARKS)
In an assembly plant the number of units produced in a day is believed to depend on the
number of workers present and the number of hours they work. The following data was
collected
Y
Units
18
7
8
10
18
19
9
7
produced
Workers 10
6
9
10
12
13
11
9
𝑋1
present
Hours
10
5
7
10
12
14
9
5
𝑋2
worked
Find the estimated regression line of Y on 𝑋1and 𝑋2
(11 marks)
Predict the number of units that would be produced if 8 workers worked for 8
hours
(4marks)
i.
ii.
QUESTION THREE (15 MARKS)
a) In a large manufacturing company an opinion survey was conducted regarding two
types of bonus schemes. Total employees were divided into two categories,
namely: laborers and executives. The results obtained by way of opinion survey
are presented in the form of contingency table as given below.
Employee categories
Technical
Executive
total
Type 1
19
30
49
Bonus schemes
Type 2
5
6
11
Total
24
36
60
Test at α= 5%, whether the opinion about bonus schemes is independent of the types of
employees
(10 marks)
b) A shop sells a particular make of radio at a rate of 4 per week on average. The
number sold in a week has a Poisson distribution.
i.
Find the probability that the shop sells at least 2 in a week
(2marks)
ii.
Find the probability that the shop does not make any sale in a week
(3marks)
QUESTION FOUR (15 MARKS)
a) Given the following data
X
1
2
3
4
5
Y
1
4
8
14
14
i.
Fit a regression line of Y on X
ii. Find the value of Y when X=3.5
6
17
7
20
8
22
9
26
10
30
(10 marks)
b) For a given se of data, the observed and expected frequencies are shown.
Result
Observed
frequency
Expected
frequency
1
30
2
31
3
42
4
40
5
57
38
45
36
36
45
Are the differences between the observed and the expected frequencies significant
at 1% level?
(5 marks)
QUESTION FIVE (15 MARKS)
a) State the errors committed when
i.
A null hypothesis is rejected when it ought to be accepted
(1 mark)
ii. A null hypothesis is accepted when it ought to be rejected
(1 mark)
b) The prices of shares of a company on different days in a month were found to be
66, 65, 69, 70, 69, 71, 70, 63, 64 and 68.
i.
Discuss whether the mean price of the shares in the month is 65 at α=5%
(7 marks)
ii. Assuming that the sample came from a normal population with variance 4,
calculate a 95% confidence interval for the mean length of all the worms in the
garden.
(3 marks)
c) The mean monthly income of 144 casual workers in a certain county is 5000 with a
standard deviation of 1200. Test the hypothesis that the monthly income of these
casual workers is 5500 (use α=0.05)
(3marks)
//END//