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Statistics for Business and Finance

Answer the following questions:
(100 Marks in total)
1.
Provide 95% confidence interval estimates for the mean
FS
(
μ
FS
)
WEF (
μ
WEF
) and
WI (
μ
WI
)
for the population of
10
00 households
based on your selected sample of
size
50 households.
(15
Marks)
2.
Test the
following
Hypothesis that
the
population
average
(i)
F
amily
S
ize is
three
.
(ii)
WI is at least $500.
(
iii)
WEF is greater than
$300
A
gainst a suitable alternative at the 10% level of significance.
What can you conclude?
(15 Marks)
3.
Estimate the following least square regression lines and explain
the meaning of the y
intercept
(b
0
)
term and the estimate
of slope
coefficients
(b
1
) in (i) and (ii) below but
(b
1
& b
2
) in (iii)
:
(i)
WEF on WI
(ii)
WEF on FS
(iii)
WEF on WI and FS
(15 Marks)
4.
Construct confidence intervals for the estimates of the slope
coefficients in (i) to (iii) of Question 3. Explain the meaning of
these confidence intervals and comment on your results about the
width of the confidence intervals, if sample size increases
from
50 to 100
.
(10
Marks)
5.
Find the values of the correlation coefficients and the coefficients
of determination, and explain thei
r meaning for the
5
0
pairs of:
(i)
WI and WEF values
(ii)
WEF and FS values
(15
Marks)
For question 6 and 7
below
please refer to
the excel file
s
(extra file
for
assignment
2
on LMS)
6.
In that
excel file
(
Oslo tab
)
,
there is 50
sample
data of Weekly
Income (WI),
Weekly Expenditure on Food (WEF) of one of the
most prosper city in the world, Oslo, Norway. Prime Minister of
Norway Erna Solberg claimed
that:
(i)
The
population average of
Weekly Income
(WI)
for her
city
is higher compared to your sample
of 50
household
s
.
(ii)
The
population mean of
Family Size (FS) for her
city
is at
least the same with your sample
of 50
household
s
.
Based on the Erna Solberg’s statement, perform the analysis on
hypothesis testing wi
th level of significance of 5%. Do you think
Erna Solberg’s sta
tement is true?
There are few assumptions that you
may
need to put in your mind,
when you perform this test:
A.
Populations for both of your sample data and
OSLO
are
normally distributed and samples are independent.
B.
Population variances for Weekly Income (WI
) are unknown
and unequal.
C.
Population variances for
FS
are unknown and equal.
(20
Marks)
7.
As
one of
the
largest city in USA, New York also known as the
food city. In this city people spend so much money in food, and
Bill de Blasio
,
Mayor of New York believe, that the
average
amount of weekly food expen
diture (WEF) spent
by households
is equal with
your sample data. In order to prove that he collects
a random sample of
50
household
s
data of his city.
(The data is
attached on
extra file
for
assignment
2
, New York t
ab)
.
Based on the Bill de Blasio’s statement, perform the analysis on
hypothesis testing with level of significance of 5%.
Do you think
Bill de Blasio’s statement is correct?
You may consider the following
assumptions
while
perform
ing
this test:
A.
Populations for both of your sample data and New York are
normally distributed and samples are not independent.
B.
Population var
iances of
Weekly Food on Expenditure (WE
F)
are unknown and unequal.
(10 Marks)
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Category: Sample Questions