PAST EXAMINATION QUESTIONS
2022 ACADEMIC YEAR
Question 1
[20]
To investigate the average amount spent each year on life insurance by individuals aged 50 or more, a
random sample of 1,000 individuals over 50 is selected. The following results are calculated from the
sample data (denoted by x): ∑ 𝑥 = 150 000
∑(𝑥 − 𝑥̅ )2 = 1 249 080
Required:
a) Develop and interpret a 95% confidence interval for the population mean.
Question 2
(20)
[20]
In a survey of 1,250 voters in a constituency, 36% stated that they intended to vote for an independent
candidate at the next election.
Required:
a) Develop and interpret a 90% confidence interval for the proportion of the population favoring an
independent candidate.
(10)
b) What sample size would be required to estimate the proportion of the population favoring an
independent candidate to be within 1% with 99% confidence?
(10)
Question 3
[20]
The owner of a retail store randomly selected the following weekly data on profits and
advertising cost:
Week
Advertising Cost (N$)
Profit (N$)
1
0
200
2
50
270
3
250
420
4
150
300
5
125
325
a) Calculate the least squares estimated regression equation.
(10)
b) Calculate and interpret the coefficient of determination.
(7)
c) Calculate the profit for a week when N$ 200 is spent on advertising.
(3)
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PAST EXAMINATION QUESTIONS
2022 ACADEMIC YEAR
Question 4
[15]
Maria a lady from Havana location in Windhoek, reported that her tuck shop makes an average
daily income of N$400. Nadia argues that Maria’s tuck shop makes more than what she’s
reported. Gerald visited his aunt Maria and recorded Maria’s tuck shop daily income for ten days
and found an average daily income of N$550 with a standard deviation of N$70.
Required:
a) Use hypotheses test at a 1% level of significance and determine what conclusion can be
reached about Maria’s tuck shop’s daily income.
(15)
Question 5
[10]
The data in the table below shows the usage of a basket of three toiletry items in a household for
December 2019 and January 2020.
December 2019
January 2020
Item
Unit Price
(N$)
Quantity
Unit Price
(N$)
Quantity
Soap
15.00
5
16.50
6
Deodorant
25.00
3
25.50
4
Lotion
Required:
50.00
2
50.25
2
a) Calculate and interpret the Laspeyres weighted aggregate price index for the basket of
toiletries for January 2020.
(6)
b) Which of the toiletries item has had the highest relative price increase between December
2019 and January 2020?
(4)
Question 6
[15]
Standard requirements for a certain drug stipulates that the variance in drug weights must not
exceed 0.035 grams (squared). A sample of five units provided the sample data as follows:
0.1
0.3
0.5
0.6
0.25
Required:
a) Use hypotheses test to determine whether the variance in the drug weights meets the
standard requirements. Use 𝛼 = 0.05
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(15)
PAST EXAMINATION QUESTIONS
2022 ACADEMIC YEAR
Question 7
[45]
As part of their project aimed at investigating the feasibility of the presumptive tax, the
Ministry of Finance selected a random sample of 26 local vendors and their sample mean
monthly income and variance was found to be N$ 7 600 and 1 250 (N$ squared),
respectively.
Required:
a) Construct and interpret the 90% confidence interval estimate for the population
mean
monthly
income
of
the
local
vendors?
(10)
b) What can be done to improve the precision of the confidence interval estimate in a)?
Discuss.
(5)
c) A representative of the local vendors argues that the local vendors‘ average monthly
income is not more than N$ 7 500. Conduct a hypothesis test at a 2.5% level of
significance to determine the validity of the claim made by the local vendors’
representative. Show all hypothesis test steps.
(15)
d) If the hypothesis test in d) was to be conducted at a level of significance greater than
2.5%, what will be the conclusion? Motivate.
QUESTION 8
(5)
[20]
Suppose a sample of 200 local vendors is selected as part of a survey conducted by the
Ministry of Trade and it is found that 145 of the local vendors make an average income in
excess of N$ 7 500 per month.
Required:
a) Suppose that a 97% confidence interval estimate of the proportion of local vendors
who make an average income less than N$ 7 500 per month is required. How large a
sample should be taken if the desired margin of error is 5%?
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(5)
PAST EXAMINATION QUESTIONS
2022 ACADEMIC YEAR
b) Suppose it has been established from past studies that 75% of local vendors make
an average income in excess of N$ 7 600 per month. Use the p-value approach and
conduct a hypothesis test at a 1% level of significance to determine whether the
proportion of local vendors who make an average income in excess of N$ 7 500 per
month differs from the historical level. Show all hypothesis test steps.
QUESTION 9
(15)
[30]
Suppose that you are assigned a task to investigate the relationship between selling price
and valuation of plots sold by a local municipality. The data below was obtained for a
random sample of seven plots.
Plot
Selling price (N$ 000) (y)
Valuation (N$ 000) (x)
1
120
72
2
100
68
3
140
72
4
150
70
5
155
75
6
100
50
7
150
58
Required:
a) Use the method of least squares and estimate the regression equation between
selling
price
and
valuation.
(15)
b) Use the estimated regression equation and make a prediction for a value of the
selling
price
when
the
valuation
is
N$
85 000.
(5)
c) Calculate and interpret the coefficient of determination.
QUESTION 10
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(10)
[5]
PAST EXAMINATION QUESTIONS
2022 ACADEMIC YEAR
An item with a price relative of 123 cost N$ 12.70 in 2021. Suppose the base year is 2016.
Required:
a) Give an interpretation of the item’s price relative.
(2.5)
b) How much did the item cost in 2016?
(2.5)
~END~
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