UNIVERSITY OF LIMPOPO
TURFLOOP CAMPUS
FACULTY OF MANAGEMENT & LAW
SCHOOL OF ECONOMICS AND MANAGEMENT
DEPARTMENT OF BUSINESS MANAGEMENT
TEST 1
MODULE:
SCMA012
(COMMERCIAL MATHEMATICS)
26 JULY
:
2019
TIME
:
PAPER
:
P1
MARKS
:
50
2 HOURS
INTERNAL EXAMINER
:
MR SS NKOANE
SECOND EXAMINER
:
PROF O FATOKI
THIS PAPER CONSISTS OF 5 PAGES INCLUDING COVER PAGE AND STATISTICAL TABLES
INSTRUCTIONS:
1. Answer all the questions
2. Write neatly and legibly
3. Show all necessary steps and calculations
SCMA012 TEST 1
2019
QUESTION 1 [10]
a. What is an inferential statistics?
(2)
b. Define and describe two general procedures for making inferences about the population.
(4)
c. What is the point estimator of population parameter?
(2)
d. What is the point estimate of population parameter?
(2)
QUESTION 2 [25]
a. The following data represent a simple random sample of 9 marks (out of 10) on a Commercial
Mathematics quiz. The marks of all students are normally distributed with a standard deviation of 2.
7,
9,
7,
5,
4,
8,
3,
10,
9
i)
Identify the point estimator of population mean.
(1)
ii)
Find 90% confidence interval, of the mean for marks of all students.
(7)
b. Determine the sample size required to estimate the population mean to within 10 units with 99%
confidence level, given that the population standard deviation is 50.
(5)
c. Determine the 90% confidence interval for population mean given the following information:
𝑥̅ = 175, 𝑠 = 30 and 𝑛 = 5
(7)
d. A statistics practitioner randomly sampled 10 observations and found 𝑥̅ = 103 and 𝑠 = 17.
Determine the maximum error with 95% confidence level.
(5)
QUESTION 3 [15]
a. A simple random sample of 400 individuals provides 100 Yes responses.
i)
What is the point estimate of the proportion of the population that would provide Yes
responses?
(1)
ii)
What is the standard error of the proportion, 𝜎𝑝̂ ?
(2)
iii)
Find the 95% confidence interval to estimate the proportion.
(7)
b. A political pollster is engaged by a politician to estimate the proportion of registered voters in her
district who plan to vote for her in the next elections. Find the sample size needed if she wants, with
at least 95% confidence, the poll to be accurate to within 8 percentage points.
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