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UNIVERSITY EXAMINATIONS: 2020/2021
EXAMINATION FOR THE DEGREE OF BACHELOR OF COMMERCE
PART TIME
DATE: AUGUST, 2020 TIME:
QUESTION ONE [25 MARKS]
a) A population consists of three numbers
6 ,3
and
9
.Consider all possible samples of
size two which can be drawn with replacement from the population. Calculate the
standard error of the sample means. [6 Marks]
b) A fair six faced die is thrown
120
times.
(i) What is the probability of exactly
32
sixes? [3 Marks]
(ii) What is the
( )
24 15 andbetweenP
sixes inclusive? [3 Marks]
(iii) Determine values of integers
1
m
and
2
m
such that there will be a
%95
probability that
there will be between
and
2
m
sixes, where
1
m
,
2
m
are on symmetrically opposite
sides of the mean. [4 Marks]
c) Suppose you wish to predict the income of University cafeterias on the basis of (a) floor
space (b) number of employees. A sample of
5
cafeterias give you the following data.
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Sample
number
Income (
y
)
(Ksh)
Floor space(
1
x
)
(
000
square feet)
No. of employees
(
2
x
)
5
4
3
2
1
000,10
000,5
000,10
000,15
000,20
2
3
10
5
10
10
7
12
8
15
Calculate the estimated regression equation. [9 Marks]
QUESTION TWO [25 MARKS]
a) The height of students in a certain computer class is distributed with mean
and standard
deviation
. A random sample of
100
students was taken and the
%90
confidence interval for
was found to be between
175
cm and
180
cm.
Estimate:
(i) Value of the sample mean; [2 Marks]
(ii) Value of
. [2 Marks]
(iii)
%95
confidence interval for
. [3 Marks]
b) Are professional jobs held in the computing industry independent of the number of years a person
has worked in the industry? Suppose
246
workers are interviewed. Use the results to obtained to
determine whether type of professional job held in the computer industry is independent of years
worked in the industry. Take
01.0=
.
Professional position
Years of
experience
Manager
programmer
operator
Systems
analysts
30
6
37
11
13
84
28
16
23
24
More than
8
47
10
12
19
[10 Marks]
c) Mwanga Digital Company has
000,5
workers. The company is interested in knowing the average
number of digital products bought per week per person by the company’s workers. While the
quality control manager thinks that the average number of digital products taken per worker per
week is
, the company secretary thinks that the true value should be more. The quality control
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manager subsequently selected workers at random and got the following results as digital products
taken per week.
6 ,21 ,20 ,18 ,12 ,9 ,17 ,14 ,6 ,5 ,19 ,17 ,11 ,20 ,15 ,9
17 ,16 ,13 ,7 ,21 ,12 ,18 ,9 ,12 ,16 ,20 ,3 ,10 ,17 ,4 ,12
Formulate a suitable hypothesis and test it at
%5
level of significance. [8 Marks]
END

### Unformatted Attachment Preview

UNIVERSITY EXAMINATIONS: 2020/2021 EXAMINATION FOR THE DEGREE OF BACHELOR OF COMMERCE STA2101: BUSINESS STATISTICS CMS301-F: ADVANCED BUSINESS STATISTICS PART TIME DATE: AUGUST, 2020 TIME: INSTRUCTIONS: Answer ALL questions showing all your workings. QUESTION ONE [25 MARKS] a) A population consists of three numbers 3, 6 and 9 .Consider all possible samples of size two which can be drawn with replacement from the population. Calculate the standard error of the sample means. [6 Marks] b) A fair six faced die is thrown 120 times. (i) (ii) What is the probability of exactly 32 sixes? What is the P(between 15 and 24) sixes inclusive? [3 Marks] [3 Marks] Determine values of integers m1 and m2 such that there will be a 95% probability that there will be between m1 and m2 sixes, where m1 , m2 are on symmetrically opposite sides of the mean. [4 Marks] c) Suppose you wish to predict the income of University cafeterias on the basis of (a) floor space (b) number of employees. A sample of 5 cafeterias give you the following data. (iii) Sample Income ( y ) Floor space( x1 ) No. of employees number (Ksh) ( 000 square feet) ( x2 ) 1 2 3 4 5 20,000 15,000 10,000 5,000 10,000 10 5 10 3 2 15 8 12 7 10 Calculate the estimated regression equation. [9 Marks] QUESTION TWO [25 MARKS] a) The height of students in a certain computer class is distributed with mean  and standard deviation  . A random sample of 100 students was taken and the 90% confidence interval for  was found to be between 175 cm and 180 cm. Estimate: (i) Value of the sample mean; [2 Marks] (ii) Value of  . [2 Marks] (iii) 95% confidence interval for  . [3 Marks] b) Are professional jobs held in the computing industry independent of the number of years a person has worked in the industry? Suppose 246 workers are interviewed. Use the results to obtained to determine whether type of professional job held in the computer industry is independent of years worked in the industry. Take  = 0.01. Professional position Years of Manager programmer operator experience Systems analysts 0−3 6 37 11 13 4−8 28 16 23 24 More than 8 47 10 12 19 [10 Marks] c) Mwanga Digital Company has 5,000 workers. The company is interested in knowing the average number of digital products bought per week per person by the company’s workers. While the quality control manager thinks that the average number of digital products taken per worker per week is 32 , the company secretary thinks that the true value should be more. The quality control manager subsequently selected workers at random and got the following results as digital products taken per week. 12, 4, 17, 10, 3, 20, 16, 12, 9, 18, 12, 21, 7, 13, 16, 17 9, 15, 20, 11, 17, 19, 5, 6, 14, 17, 9, 12, 18, 20, 21, 6 Formulate a suitable hypothesis and test it at 5% level of significance. END [8 Marks] Name: Description: ...
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