TUTORIAL 8
INCEIF
The Global University in Islamic finance
Kuala Lumpur, Malaysia
MASTERS IN ISLAMIC FINANCE PRACTICE (MIFP)
Assignment for
QM5013 QUANTITATIVE ANALYSIS "Topic " Tutorial EIGHT Answers
Semester June, 2014
Facilitator: PROF. Assoc. Prof Dr. Baharom Abd Hamid Name: MUSTAFA KASSIM AHMED
ID: 1100386
TUTORIAL 8
QUANTITATIVE ANALYSIS
QUESTION 1:
A sample of 40 observations is selected from one population with a population standard deviation of 5. The sample mean is 102. A sample of 50 observations is selected from a second population with a population standard deviation of 6. The sample mean is 99. Conduct the following test of hypothesis using the .04 significance level.
H0: μ1 = μ2
H1: μ1 ≠ μ2
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule
c. Compute the value of the test statistic
d. What is your decision regarding H0?
e. What is the p-value?
Solution
Given: n1 =40, 1 = 5, x̄1= 102, n2 = 50, 2 = 6, x̄2 = 99, = 0.4
a. Two tailed.
b. Since = 0.04 and critical point = 2.05, reject H0, if computed z > 2.05 or –z < -2.05
c. Z= = = 2.59
d. The H0 is rejected because the computed z > critical value of 2.05.
e. P-value = P (Z > 2.05) = 0.5- 0.4798= 0.0202, since this is less than the value, H0 is rejected.
QUESTION 2:
A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level.
H0: μ1 ≤ μ2
H1: μ1 > μ2
a. Is this a one-tailed or a two tailed test?
b. State the decision rule
c. Compute the value of the test statistic
d. What is your decision regarding H0?
e. What is the p-value?
Solution
Given: n1 =65, 1 = 0.75, x̄1= 2.67, n2 = 50, 2 = 0.66, x̄2 = 2.59, = 0.08
a. It is one tailed.
b. Since = 0.08
The Global University in Islamic finance
Kuala Lumpur, Malaysia
MASTERS IN ISLAMIC FINANCE PRACTICE (MIFP)
Assignment for
QM5013 QUANTITATIVE ANALYSIS "Topic " Tutorial EIGHT Answers
Semester June, 2014
Facilitator: PROF. Assoc. Prof Dr. Baharom Abd Hamid Name: MUSTAFA KASSIM AHMED
ID: 1100386
TUTORIAL 8
QUANTITATIVE ANALYSIS
QUESTION 1:
A sample of 40 observations is selected from one population with a population standard deviation of 5. The sample mean is 102. A sample of 50 observations is selected from a second population with a population standard deviation of 6. The sample mean is 99. Conduct the following test of hypothesis using the .04 significance level.
H0: μ1 = μ2
H1: μ1 ≠ μ2
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule
c. Compute the value of the test statistic
d. What is your decision regarding H0?
e. What is the p-value?
Solution
Given: n1 =40, 1 = 5, x̄1= 102, n2 = 50, 2 = 6, x̄2 = 99, = 0.4
a. Two tailed.
b. Since = 0.04 and critical point = 2.05, reject H0, if computed z > 2.05 or –z < -2.05
c. Z= = = 2.59
d. The H0 is rejected because the computed z > critical value of 2.05.
e. P-value = P (Z > 2.05) = 0.5- 0.4798= 0.0202, since this is less than the value, H0 is rejected.
QUESTION 2:
A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level.
H0: μ1 ≤ μ2
H1: μ1 > μ2
a. Is this a one-tailed or a two tailed test?
b. State the decision rule
c. Compute the value of the test statistic
d. What is your decision regarding H0?
e. What is the p-value?
Solution
Given: n1 =65, 1 = 0.75, x̄1= 2.67, n2 = 50, 2 = 0.66, x̄2 = 2.59, = 0.08
a. It is one tailed.
b. Since = 0.08