ECON1203
Business and Economics Statistics
Tutorial 6 Problems
Week 7
1. In a certain large city, household annual incomes are considered approximately
normally distributed with a mean of $40,000 and a standard deviation of $6,000. What
proportion of hous
ECON1203
Business and Economics Statistics
Proposed solutions to Tutorial Problem 7
Week 8
1. Suppose a normally distributed random variable X has a mean of 50 and a variance of 100.
Also suppose a sample of size 16 is drawn from this population. Calculat
Sampling and Estimation Revision
1.a
2.a
2.b
Expected value or mean of x is the mean of all possible values of x that can be generated by simple
random samples. In this case E( x ) 750 (gm) ie the mean of all possible means is equal to the mean
of the pop
FIN10002 Revision
REGRESSION, TIME SERIES and INDEX NUMBERS
1.
The management of a building society in the city of Mortgageville would like to know
how house sales vary with interest rates. The following table shows the average home
mortgage interest rate
FIN10002 Revision
Probability and Normal Probability
1. An airline has offered a special vacation package to Fiji. The length of stay is either for 3
days or 7 days, and the type of accommodation can be either economy, regular, or deluxe.
Consider the exp
FIN10002 Revision
HYPOTHESIS TESTING
1 A bath soap manufacturing process is designed with the expectation that each batch prepared
in the mixing department will produce a mean of 120 bars of soap per batch. Quantities over or
under this standard are undes
HYPOTHESIS TESTING REVISION
SOLUTIONS
All answers are given in short but you must provide your answers in 5-step procedure as indicated in
notes. In all questions was used as 5%.
Qu 1 Two tail test, t calculated =-0.7053, df=9, t critical is +2.262 and -2
1.
Supplier B
Supplier A
Event
Prob
0.65
0.45
On time
0.55 0.65 = 0.3575
(L, OT)
0.45 0.35 = 0.1575
0.45 0.65 = 0.2925
Late
0.35
0.55 0.35 = 0.1925
(L, L)
0.65
0.55
On time
(OT, OT)
(OT, L)
0.35
Late
On time
Late
SUM
(a)
Pr(Both on time) = Pr(OT, OT) = 0.
Revision questions for Exam
1. A purchasing agent has placed two rush orders for a particular raw material from two
different suppliers, A and B. If neither order has arrived in 4 days the production process
must be shut down until at least one of the ord
Revisions for Unit 1: Financial Mathematics
1
a
He needs to invest $2547.47 per month
b
10.25 years
2
a i
ii
iii
$986.57 per month
Total payments=986.57*25*12=$295,971
Total interest paid=$295, 971-120, 000=$175, 971
Total payments=986.57*25*12=$295,971
b
Financial Statistics
FIN 10002
FIN10002 revision for Financial mathematics
1.
(a) A person wishes to retire on a lump sum of $500,000 in 10 years time. He is able to invest
his money at 9.25% pa compounded monthly. How much per month should he invest in o
FIN1002 Financial Statistics Module 8 Time Series Solutions 2015/16
Set 8A
Question 1
(a)
Enter the data into three columns in an Excel spreadsheet say column A, column B and column C.
Highlights cells B2 to C12, click the insert tab at the top of the spr
FIN1002 Financial Statistics Module 7 Correlation and Regression
Solutions 2015/16
Question 1
(a)
Enter the data into two columns in an Excel spreadsheet say column A and column B. Highlights cells
A2 to B11, click the insert tab at the top of the spreads
FIN1002 Financial Statistics Module 6 Sampling Solutions Set 5B- 2015/16
Solutions for Set 6A
Question 1
i.
Null Hypothesis
Alternative Hypothesis
ii.
Test Statistic and significance: Z-test ( population standard deviation is known) and
=0.05
1175012000
FIN1002 Financial Statistics Module 5 Sampling Solutions Set 5B- 2015/16
1
Calculate the margin of error
Therefore the lower limit=11750-196.00=11,554
The upper limit=11750+196.00=11, 946
95 % confidence interval for the population mean is (11, 554, 11,94
FIN1002 Financial Statistics Module 5 Sampling Solutions Set 5A2015/16
1.
The purpose of statistical inference is to obtain information about a population parameter based
on a subsection of the population called a sample.
2.
Population
p
Mean
Standard dev
SOLUTIONS FOR NORMAL DISTRIBUTION EXERCISES
SET 4B:
1.
(iv)
Pr(10 < X < 27)
=normdist(27,20,5,true) normdist(10,20,5,true)
= 0.896 i.e. 89.6%
(a) (i)
Pr(5 < X < 35)
= normdist(35,20,5,true)normdist(5,20,5,true)
= .997
i.e. 99.7%
(v)
Pr(7 < X < 17)
=normdi
SOLUTIONS TO EXERCISES ON NORMAL DISTRIBUTION
SET 4A:
1.
3. (a) For Q3 to Q7 use Excel to calculate the
probabilities. You should also draw some of the
diagrams by hand BEFORE using Excel to
calculate the probability.
2. (a) P(z 1) = normsdist(1) = 0.159
Financial Statistics
FIN 10002
SOLUTIONS:
SET 2A:
(a)
Ratio/discrete
(c)
ratio/continuous
(b)
(d)
nominal
ratio/continuous
SET 2B:
(a)
The variable is student learning style. This is a nominal variable.
(b)
(i)
Pie chart of Preferred Learning Styles
Serie
Exercise Set 1A
Q1
FV is used
Future value= $64845.30
Q2
PV is used
Q3
Present value= $62346.89
NPER is used
Q4
Number of years= 5.29 years
EFFECT is used
Effective interest rate is 0.0439*100%=4.39% per annum
Q5 a
EFFECT is used
Effective interest rate i
Associations
When one variable, y, increases with the second variable, x, there is a positive
association between x and y
When one variable decreases with the second variable, there is a negative association
When y increases as x decreases, there is a neg