FINC 7301: Midterm Examination on Statistical Methods and Analysis

This document presents a solved midterm examination for FINC 7301, focusing on research and quantitative methods. The exam includes three questions. The first question involves a z-test to determine if the mean share price return is greater than 30%, given a sample of returns and a standard deviation. The second question uses a t-test to compare the mean cash waqf returns of two states, Negeri Sembilan and Selangor, assuming equal population standard deviations. The solution provides step-by-step calculations, including the formulation of hypotheses, determination of critical values, calculation of test statistics, and interpretation of results. The third question requires the identification and explanation of two characteristics of the F-distribution. The solution provides detailed calculations and explanations for each step of the problem, demonstrating the application of statistical concepts in a financial context.

FINC 7301 Research and Quantitative Methods
Midterm Examination
8pm – 11pm
40 marks
Instructions:
1. Answer all questions.
2. Show all the mathematical workings so marks can be given accordingly.
3. You may answer using Microsoft Word or even using pen and paper. However,
submission must be in PDF format.
4. Submit your answer at iTa’leemc course page > Assignment, Project, and Examination
> Midterm Examination Submission. Should the server of iTa’leemc is down, you may
submit your answers to [e-mail].
Question 1
Pyramidia Sdn. Bhd. provides a return of 30% per share. According to historical data, the share
price return follows the normal distribution and the standard deviation of the share price is 8%.
At the end of the trading day, Chandra calculates the sample mean of the share price. The
sample returns of the share price are 10%, 20%, 30%, 40%, 45%, and 50%. Using the 0.1
significance level, can Chandra conclude that the mean of the share price return is more than
30%? [13 marks]
Step 1:
H0: μ ≤ 0.3 [1 mark]
H1: μ > 0.3 [1 mark]
Step 2:
α = 0.1 [1 mark]
Step 3:
Test statistic used is z [1 mark]
Step 4:
One-tailed test (right tail) [1 mark]
Using the t-test table, at α = 0.1, the critical value is 1.282 [1 mark]
Step 5:

𝑥̅ = 0.1 + 0.2 + 0.3 + 0.4 + 0.45 + 0.5
6 = 0.325
[2 marks]
𝑧 =𝑥̅− 𝜇
𝜎
√𝑛⁄ = 0.325 − 0.3
0.08
√6
⁄ = 0.7655
[2 marks]
Since 0.7655 < 1.282, do not reject H0. [2 marks]
Step 6:
The sample information fails to indicate that the mean return is greater than 30% [1 mark]
Question 2
Aidil works for Yayasan Waqaf Malaysia. He is analyzing the cash waqf return of two states
namely Negeri Sembilan and Selangor. The data provided from the two states are as follows:
Negeri Sembilan Selangor
5% 3%
10% 13%
15% 15%
20% 25%
25%
At the 0.1 significance level, can Aidil conclude that the mean returns of Negeri Sembilan are
greater than or equal to Selangor? Aidil assumes that the population standard deviation for both
states are equal. [22 marks]
Assuming N represents Negeri Sembilan and S represents Selangor;
Step 1:
H0: μN ≥ μS [1 mark]
H1: μN < μS [1 mark]
Step 2:
α = 0.1 [1 mark]
Step 3:
Test statistic used is t because σ is not known and sample size is less than 30 [1 mark]
Step 4:
One-tailed test (left tail) [1 mark]

df = n1 + n2 – 2 = 5 + 4 – 2 = 7 [1 mark]
Using the t-test table, at α = 0.1, the critical value is -1.415 [1 mark]
Step 5:
𝑁̅= 0.05 + 0.1 + 0.15 + 0.2 + 0.25
5 = 0.15
[2 marks]
𝑠𝑁
= √(0.05 − 0.15)2 + (0.1 − 0.15)2 + (0.15 − 0.15)2 + (0.2 − 0.15)2 + (0.25 − 0.15)2
5 − 1
= 0.079057
[2 marks]
𝑆̅ = 0.03 + 0.13 + 0.15 + 0.25
4 = 0.14
[2 marks]
𝑠𝑆 = √(0.03 − 0.14)2 + (0.13 − 0.14)2 + (0.15 − 0.14)2 + (0.25 − 0.14)2
4 − 1 = 0.090185
[2 marks]
𝑠𝑝
2 = (5 − 1)(0.079057)2 + (4 − 1)(0.090185)2
7 = 7.05715 × 10−3
[2 marks]
𝑡 = 0.15 − 0.14
√7.05715 × 10−3 (1
5 + 1
4)
= 0.177451
[2 marks]
Since 0.177451 > -1.415, do not reject H0 [2 marks]
Step 6:
The sample information indicates that there is some evidence that the mean returns of Negeri
Sembilan are greater than or equal to Selangor [1 mark]
Question 3
State two characteristics of the F distribution. Provide a brief explanation for each of the
characteristics. [5 marks] Answer in the textbook