Quantitative Methods for Business, Finance Assignment on Inflation

This homework assignment analyzes inflation rates in two countries (A and B) across different time periods using various statistical methods. The assignment begins by presenting descriptive statistics of inflation, including mean, standard deviation, median, minimum, and maximum values. It then calculates confidence intervals for the population mean inflation rates for both countries using the t-score. Furthermore, the assignment conducts one-sample t-tests to determine if the mean inflation rates of country A and B meet specific criteria, such as being equal to a certain percentage or less than a certain percentage. Independent and paired sample t-tests are also performed to compare inflation rates between different periods and countries. Finally, the assignment explores probability calculations related to inflation rates and determines the proportion of years with inflation rates exceeding a certain threshold. The student demonstrates a strong understanding of statistical concepts and their application in financial analysis.

Running Head: QUANTITATIVE METHODS FOR BUSINESS
Quantitative Methods for Business
Name of the Student
Name of the University
Author Note

1QUANTITATIVE METHODS FOR BUSINESS
Answer 1
Mean
inflation
Standard
deviation
of inflation
Median
inflation
Minimum
inflation
Maximum
inflation
Country A
1980-1999 2.57 1.88 2.30 -0.50 7.30
2000-2010 2.02 5.78 98.97 88.14 106.99
Country B
1980-1999 1.64 1.97 1.12 -1.24 7.47
2000-2010 -0.34 0.83 -0.40 -1.77 0.90
Answer 2
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
Inflation Rate of Netherlands
Year
Inflation Rate

2QUANTITATIVE METHODS FOR BUSINESS
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
-4.00
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
Inflation Rate of Japan
Year
Inflation Rate
Answer 3
The inflation rates of the countries A and B are normally distributed. The confidence
intervals of normal distributions are given by the following formula:
μ ± t∗σ
√ n
Here, μ is the sample mean, σ is the sample variance, n is the sample size and z is the standard
value of the t score obtained from the t-table according to the level of significance of the
confidence interval and the degrees of freedom.
For 90% confidence interval, the t-score = 1.729
For 95% confidence interval, the t-score = 2.093
For 99% confidence interval, the t-score = 2.861

3QUANTITATIVE METHODS FOR BUSINESS
a) The 95% confidence interval for the population mean inflation rate of country A,
Netherlands, is given by:
(μ−t∗σ
√ n , μ+ t∗σ
√ n )
= (2.57 – 2.093 * 1.88
√ 20 ,2.57 +2.093 * 1.88
√ 20 )
= (1.69, 3.45)
From here, it can be said with 95% confidence that the population mean inflation
rate will lie between 1.69 and 3.45
b) The 99% confidence interval for the population mean inflation rate of country A,
Netherlands, is given by:
(μ−t∗σ
√ n , μ+ t∗σ
√ n )
= (2.57 – 2.861 * 1.88
√ 20 ,2.57 + 2.861 * 1.88
√ 20 )
= (1.37, 3.77)
From here, it can be said with 99% confidence that the population mean inflation
rate will lie between 1.37 and 3.77
c) The 95% confidence interval for the population mean inflation rate of country B,
Japan, is given by:
(μ−t∗σ
√ n , μ+ t∗σ
√ n )
= (1.64 – 2.093 * 1.97
√ 20 ,1.64 + 2.093 * 1.97
√20 )
= (0.72, 2.56)

4QUANTITATIVE METHODS FOR BUSINESS
From here, it can be said with 95% confidence that the population mean inflation
rate will lie between 0.72 and 2.56.
d) The 90% confidence interval for the population mean inflation rate of country B,
Japan, is given by:
(μ−t∗σ
√ n , μ+ t∗σ
√ n )
= (1.64 – 1.729 * 1.97
√ 20 ,1.64 + 1.729 * 1.97
√20 )
= (0.88, 2.40)
From here, it can be said with 95% confidence that the population mean inflation
rate will lie between 0.88 and 2.40
Answer 4
a) To test whether the mean inflation of country A (Netherlands) throughout the
period 1980-2010 was 3% or not, one sample t-test has to be conducted. The null and
alternate hypothesis for the t-test can be given as,
H0: μ = 3
H1: μ≠ 3
Here, μ is the population mean which has to be estimated.
The sample mean (X ) = 2.38
The sample standard deviation (s) = 1.61
Number of observations (n) = 20
Degrees of freedom (n – 1) = 19
The required test statistic for the test is given by the following formula:

5QUANTITATIVE METHODS FOR BUSINESS
t= X−μ
s
√ n
Therefore, t =
2.38−3
1.61
√20
= -1.7222
The tabulated value of t (both tailed test) with 19 degrees of freedom at 0.05 level
of significance is 2.093. The absolute value of the observed value of t-statistic is less than
the tabulated value of the t-statistic. Thus, the null hypothesis is accepted. Hence, it can
be said that there is enough evidence to support the claim that the mean inflation
throughout the period 1980-2010 was 3%.
b) To test whether the mean inflation of country B (Japan) throughout the period
2000-2010 was less than 3.5% or not, one sample t-test has to be conducted. The null and
alternate hypothesis for the t-test can be given as,
H0: μ≥ 3.5
H1: μ< 3.5
Here, μ is the population mean which has to be estimated.
The sample mean (X ) = -0.34
The sample standard deviation (s) = 0.83
Number of observations (n) = 20
Degrees of freedom (n – 1) = 19
The required test statistic for the test is given by the following formula:
t= X−μ
s
√ n

6QUANTITATIVE METHODS FOR BUSINESS
Therefore, t =
−0.34−3.5
0.83
√ 20
= -20.6904
The tabulated value of t (both tailed test) with 19 degrees of freedom at 0.05 level
of significance is 2.093. The absolute value of the observed value of t-statistic is more
than the tabulated value of the t-statistic. Thus, the null hypothesis is rejected. Hence, it
can be said that there is not enough evidence to support the claim that the mean inflation
throughout the period 2000-2010 was 3.5%.
c) To test whether the mean inflation of country A (Netherlands) throughout the 11-
year period of euro membership 2000-2010 was significantly less than the mean inflation
of country A (Netherlands) throughout the 20-year period before euro membership 1980-
1999, independent sample t-test has to be conducted. The null and alternate hypothesis
for the t-test can be given respectively as,
H0: μ1 = μ2
H1: μ1 ≠ μ2
Here, μ1 is the population mean for the period 1980-1999 and μ2 is the population mean
for the period 2000-2010.
The sample mean for the period 1980-1999 ( X1) = 2.57
The sample mean for the period 2000-2010 ( X2) = 2.02
The sample standard deviation for the period 1980-1999 (s1) = 1.88
The sample standard deviation for the period 2000-2010 (s2) = 5.78
Number of observations for the period 1980-1999 (n1) = 20
Number of observations for the period 2000-2010 (n2) = 11
Degrees of freedom (v) = n1 + n2 -1 = 20 + 11 -1 = 30

7QUANTITATIVE METHODS FOR BUSINESS
The required test statistic for the test is given by the following formula:
t= ( X1− X2 )−( μ1−μ2 )
√ s1
2
n1
+ s2
2
n2
Therefore, t = 0.55−0
1.79 = 0.3068
The tabulated value of t (both tailed test) with 30 degrees of freedom at 0.05 level
of significance is 2.042. The absolute value of the observed value of t-statistic is less than
the tabulated value of the t-statistic. Thus, the null hypothesis is accepted. Hence, it can
be said that there is enough evidence to support the claim that the mean inflation
throughout the period 2000-2010 does not differ significantly with the period 1980-1999.
d) To test whether the mean inflation of country A (Netherlands) throughout the 11-
year period of euro membership 2000-2010 was significantly less than the mean inflation
of country B (Japan) throughout the 11-year period of euro membership 2000-2010,
paired sample t-test has to be conducted.
Let z be defined as (observation of country A) – (observation of country B)
The null and alternate hypothesis for the t-test can be given respectively as,
H0: μz ¿ 0
H1: μz ≠ 0
Here, μz is the population mean which has to be estimated.
The sample mean ( z) = 2.36
The sample standard deviation (s) = 1.46
Number of observations (n) = 20
Degrees of freedom (n – 1) = 10

8QUANTITATIVE METHODS FOR BUSINESS
The required test statistic for the test is given by the following formula:
t= z−μz
s
√n
Therefore, t = 5.094
The tabulated value of t (both tailed test) with 10 degrees of freedom at 0.05 level
of significance is 2.288. The absolute value of the observed value of t-statistic is less than
the tabulated value of the t-statistic. Thus, the null hypothesis is accepted. Hence, it can
be said that there is enough evidence to support the claim that the mean inflation
throughout the period 2000-2010 for country A and country B does not differ
significantly.
Answer 5
The population mean and population variance for country C is same as that of country A.
Let the inflation rate of country C be denoted by S
a) Therefore, P (S < 1.5) = P ( S−2.02
5.78 < 1.5−2.02
5.78 ¿=P ( Z ←0.09 )=0.46
b) Therefore, P (S > 2.5) = P ( S−2.02
5.78 < 2.5−2.02
5.78 ¿=P ( Z ←0.09 )=0.53

9QUANTITATIVE METHODS FOR BUSINESS
Answer 6
In the period of 1980-1999, the number of years in which the country B’s inflation rate is
greater than 5% is 1
Therefore, the proportion of years (p) = (1/20) = 0.05
Let the inflation rate of country D be denoted by T
a) Therefore, P (T > 0.05) = P (
T −1.64
1.97
√ 6
< 0 . 0 5−1.64
1.97
√ 6
¿=P ( Z ←1.98 ) =0.02
b) Therefore, P (T > 0.33) = P (
T −1.64
1.97
√ 6
< 0 . 33−1.64
1.97
√ 6
¿=P ( Z ←1.63 ) =0.05