UNIVERSITY OF LIMPOPO
FACULTY OF MANAGEMENT & LAW
SCHOOL OF ECONOMICS AND MANAGEMENT
DEPARTMENT OF BUSINESS MANAGEMENT
TEST 2
MODULE: SCMA012 30 AUGUST : 2019
(COMMERCIAL MATHEMATICS)
TIME : 2 HOURS MARKS : 60
INTERNAL EXAMINER : MR SS NKOANE
SECOND EXAMINER : PROF O FATOKI
THIS PAPER CONSISTS OF 9 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 2 2019
QUESTION 1 [10]
a) Define the following terms:
i) Significance level. (1)
ii) Confidence level. (1)
b) Describe three possible choices of an alternative hypothesis for population mean. (3)
c) What the purpose of hypothesis process? (1)
d) Suppose that a hypothesis test is conducted at a small significance level. Give two possible
conclusions. (4)
QUESTION 2 [28]
a) A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not
exceed 3%. It is known that from a particular production run impurity concentrations follow a
normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a
production run was checked, and the sample mean impurity concentration was found to be 3.07%.
Find the p-value for the right tailed test. (5)
b) A federal agency responsible for enforcing laws governing weights and measures routinely laws
governing weights and measures routinely inspects packages to determine whether the weight of
the contents is at least as greater as that advertised on the package. A random sample 18
containers whose packaging states that the contents weigh 8 kilograms was drawn. The contents
were weighed and the results follow.
7.80 7.91 7.93 7.99 7.94 7.75 7.97 7.95 7.79 8.06 7.82 7.89 7.92 7.87
7.92 7.98 8.05 7.91
Can we conclude at the 1% significance level that on average the container are mislabeled? (13)
c) Of 1053 SA adults who were asked whether they favoured or opposed passage of new 800 billion
rand economic stimulus package, 548 said that they fovoured passage. At the 5% significance
level, do the data provide sufficient evidence to conclude that a majority of SA adults favoured
passage? (10)
1|Page
FACULTY OF MANAGEMENT & LAW
SCHOOL OF ECONOMICS AND MANAGEMENT
DEPARTMENT OF BUSINESS MANAGEMENT
TEST 2
MODULE: SCMA012 30 AUGUST : 2019
(COMMERCIAL MATHEMATICS)
TIME : 2 HOURS MARKS : 60
INTERNAL EXAMINER : MR SS NKOANE
SECOND EXAMINER : PROF O FATOKI
THIS PAPER CONSISTS OF 9 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 2 2019
QUESTION 1 [10]
a) Define the following terms:
i) Significance level. (1)
ii) Confidence level. (1)
b) Describe three possible choices of an alternative hypothesis for population mean. (3)
c) What the purpose of hypothesis process? (1)
d) Suppose that a hypothesis test is conducted at a small significance level. Give two possible
conclusions. (4)
QUESTION 2 [28]
a) A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not
exceed 3%. It is known that from a particular production run impurity concentrations follow a
normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a
production run was checked, and the sample mean impurity concentration was found to be 3.07%.
Find the p-value for the right tailed test. (5)
b) A federal agency responsible for enforcing laws governing weights and measures routinely laws
governing weights and measures routinely inspects packages to determine whether the weight of
the contents is at least as greater as that advertised on the package. A random sample 18
containers whose packaging states that the contents weigh 8 kilograms was drawn. The contents
were weighed and the results follow.
7.80 7.91 7.93 7.99 7.94 7.75 7.97 7.95 7.79 8.06 7.82 7.89 7.92 7.87
7.92 7.98 8.05 7.91
Can we conclude at the 1% significance level that on average the container are mislabeled? (13)
c) Of 1053 SA adults who were asked whether they favoured or opposed passage of new 800 billion
rand economic stimulus package, 548 said that they fovoured passage. At the 5% significance
level, do the data provide sufficient evidence to conclude that a majority of SA adults favoured
passage? (10)
1|Page
