mas202 group assignment description of sample data

Introduction to the parameters of interest parametersThis time, we have collected stock prices of FPT and Vinamilk VNM from April 1, 2022 to October 31, 2022.. The parameters that we are

MAS202 GROUP ASSIGNMENT –

Class: MKT1613

Lecture: Nguyen Viet Anh

Subject: MAS202

Group Group 05 :

STUDENT INFORMATION

FOR TEACHER ONLY

(NAME AND SIGNATURE)

TABLE OF CONTENT

-

I INTRODUCTION

II COLLECTING SAMPLE DATA

1 State how to get data, cite data sources

2 Explain why this data makes sense for the problem

3 Attach a link to an Excel file containing data and calculations III DESCRIPTION OF SAMPLE DATA

1 Calculate the important statistics: mean, standard deviation, Q1, Q2, Q3

2 Draw appropriate charts to summarize sample data: column charts, box charts, etc

IV CALCULATION

1 Problem 1: Find a Confidence Interval

2 Problem 2: Hypothesis testing

3 Problem 3: Linear regression

V CONCLUSION

I INTRODUCTION

1 Introduction to the population of interest (population)

Currently, the demand for learning about the stock market is extremely high Because everyone wants to be able to achieve their goals of financial freedom, or simply increase their savings and generate passive income Understanding the needs as well as the benefits

of learning about and investing in securities early, we have collected information about the stock price of FPT Corporation and Vinamilk Corporation to conduct an analysis From the results of the analysis, we will have a platform to compare and select potential stocks

to make investment decisions

2 Introduction to the parameters of interest (parameters)

This time, we have collected stock prices of FPT and Vinamilk (VNM) from April 1, 2022

to October 31, 2022 The parameters that we are interested in are the opening price, the highest price, the lowest price, and the closing price of a trading session (most interested

in the closing price of two stocks)

3 Summary of results

− Use “Confidence interval” to estimate stock price more than 75,000 VND of FPT

and VNM

− Use the “T-test” to compare the closing price and opening price of FPT stock and VNM stock

− Use the “Linear Regression Equation” to examine the relationship between stock

trading volume and the closing price on the same day of FPT stock

II COLLECTING SAMPLE DATA

1 State how to get data, cite data sources

Get data on the stock prices of two companies from April 1, 2022 to October 31, 2022 Data source:

− About FPT Stock price: Click here!

− About VNM Stock price: Click here!

2 Explain why this data makes sense for the problem

To be able to maximize profits and minimize risks, any investor needs to source information from the past to the present time and evaluate them to make the best choice for them Therefore, we will need to analyze the stock price data of both stocks that have to be selected in the appropriate time period to be able to make the most reasonable investment decision The data selected by the group is secondary data that has been announced by the two enterprises themselves and verified to make the calculation more accurate

3 Attach a link to an Excel file containing data and calculations

https://docs.google.com/spreadsheets/d/1An-8cLJG9UOBIH_VQfYBj6FjW7tpxGJA/edit?usp=share_link&ouid=1019228942491

49025150&rtpof=true&sd=true

III DESCRIPTION OF SAMPLE DATA

1 Calculate the important statistics: mean, standard deviation, Q1, Q2, Q3

• About FPT Stock

Content

FPT Opening price

(x1000)

Highest price (x1000)

Lowest price (x1000)

Closing price (x1000) Mean 90,97278912 92,32585034 89,55646259 90,80884354 Standard Error 1,017634814 1,070189363 0,987092199 1,037157002

Standard

Deviation (S) 12,33816641 12,97535645

11,96785688

12,57486036 Sample Variance 152,2303504 168,3598751 143,2295984 158,127113

t( /2) 1,976345655 1,976345655 1,976345655 1,976345655

• About Vinamilk (VNM) Stock

Opening price (x1000)

Highest price (x1000)

Lowest price (x1000)

Closing price (x1000) Mean 73,14013605 74,08843537 72,3979592 73,18163265 Standard Error 0,271053505 0,256824687 0,27488693 0,265854147

Standard

Deviation (S) 3,286349098 3,113833848 3,33282696 3,223310228 Sample Variance 10,80009039 9,695961234 11,1077355 10,38972882

t( /2) 1,976345655 1,976345655 1,976345655 1,976345655

2 Draw appropriate charts to summarize sample data: column charts, box charts, etc

• About FPT Stock

➔ From the chart, we can see that FPT's stock price fluctuated quite strongly in mid-June and generally tended to decrease

• About Vinamilk (VNM) Stock

➔ From the chart, we can see that Vinamilk's stock price tends to fluctuate month by month, and is currently trending up

• About the chart of the closing price of 2 stocks

➔ The chart above shows the closing price of 2 stocks changing day by day (from April 1, 2022 to October 31, 2022)

IV CALCULATION

1 Problem 1: Find a Confidence Interval

1.1 Determine a 95% confidence interval for the closing price of FPT shares is more than 75,000 VND

Sample data is the closing price of FPT shares more than 75,000 VND for 7 months (from April 1, 2022 to October 31, 2022)

1- = 0.95 => = 0.05 α α => α/2 = 0.025 => z( /2) = 1.96 α

CONFIDENCE INTERVAL (95%)

Conclusion: We are 95% confident that the closing price of FPT shares more than 75,000 VND is between 86.567% and 95.746%

1.2 Determine a 95% confidence interval for the closing price of VNM shares is more than 75,000 VND

Sample data is the closing price of VNM shares more than 75,000 VND for 7 months (from April 1, 2022 to October 31, 2022)

1- = 0.95 => = 0.05 α α => α/2 = 0.025 => z( /2) = 1.96 α

CONFIDENCE INTERVAL (95%)

Lower point 23.162%

Conclusion: We are 95% confident that the closing price of VNM shares is more than 75,000 VND between 23.162% and 38.063%

2 Problem 2: Hypothesis testing

2.1 At the 5% level of significance, is there any evidence that there is a

difference in the opening price between FPT stock and VNM stock?

𝐻0: μFPT - μVNM = 0

𝐻1: μFPT - μVNM ≠ 0 (Two-tail test)

Sample size: 1 = 2 =147 The significance level is 0,05 (𝑛 𝑛 α=0,05), df= 1 + 2 2=292 𝑛 𝑛 –

Since σ1 and σ2 are unknown, assume equal Use to estimate the unknown 𝑆𝑝 σ

=> Use Pooled-Variance t test

Pooled variance is:

𝑆𝑝2=(𝑛1 −1)𝑆 1 +(𝑛 2 −1)𝑆 2

( 𝑛 −1 1 ) +(𝑛 2 −1) =(147−1) 12 342+(147−1)3.2862

(147 −1)+( 147 −1) = 81.52 The test statistic is:

𝑡𝑆𝑇𝐴𝑇=(𝑋1 −𝑋 2 )−(𝜇 −𝜇 ) 1 2

√𝑆 𝑝2(1

𝑛1 +1𝑛2) =(90 97 − 73 14)−0

√ 81 52(1147+1

147 )= 16.93 𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 = 𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙= 𝑡(∝

2 ;𝑑𝑓)= 𝑡(0.025 292); = 1.968

𝑡𝑆𝑇𝐴𝑇> 𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙> −𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙=> Reject H0

Conclusion: At the 5% level of significance, there is sufficient evidence that there is a difference in the opening price between FPT stock and VNM stock

2.2 At the 5% level of significance, is there any evidence that there is a difference in the closing price between FPT stock and VNM stock?

𝐻0: μFPT - μVNM = 0

𝐻1: μFPT - μVNM ≠ 0 (Two-tail test)

Sample size: 1 = 2 =147 The significance level is 0,05 (𝑛 𝑛 α=0,05), df= 1 + 2 2=292 𝑛 𝑛 –

Since σ1 and σ2 are unknown, assume equal Use to estimate the unknown 𝑆𝑝 σ

=> Use Pooled-Variance t test

Pooled variance is:

𝑆𝑝 2=(𝑛1 −1)𝑆 1 +(𝑛 2 −1)𝑆 2

( 𝑛 −1 1 ) +(𝑛 2 −1) =(147−1) 12 5752+(147−1)3.222

(147 −1)+( 147 −1) = 84.25 The test statistic is:

𝑡𝑆𝑇𝐴𝑇=(𝑋1 −𝑋 2 )−(𝜇 −𝜇 ) 1 2

√𝑆 𝑝2(1𝑛1+1

𝑛2 ) =(90.8− 73 18)−0

√ 84 25(1147+1

147 )= 16.463 𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 = 𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙= 𝑡(∝

2 ;𝑑𝑓)= 𝑡(0 025 292) ; = 1.968

𝑡𝑆𝑇𝐴𝑇> 𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙> −𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙=> Reject H0

Conclusion: At the 5% level of significance, there is sufficient evidence that there is a difference in the closing price between FPT stock and VNM stock

3 Problem 3: Linear regression

The two variables X and Y are FPT stock trading volume and the closing price of FPT stock on the same day

Sample data are the FPT stock trading volume and the closing price of FPT stock in 7 months (from April 1, 2022 to October 31, 2022)

R Square = 44.2% is enough to predict the closing price of FPT stock through FPT stock trading volume on the same day

Regression has a linear relationship between the independent variable and the dependent variable 44.2% of the variation in the closing price of FPT stock was explained by the FPT stock trading volume

From excel, we are:

r² = 1 −𝑛−1

𝑛−𝑘 = 0.442

Sx = 𝑋𝑖+𝑋𝑛

𝑛 1989 =

𝜎=√∑𝑛𝑖=1(𝑋𝑖−𝑋) 2

𝑛−1 1060.75 =

Sy = 𝑋𝑖+𝑋𝑛

𝑛 91 =

𝜎= √∑𝑛𝑖=1(𝑋𝑖−𝑋)2

𝑛−1 12.6 =

𝛽0 = 𝜎𝑦 − 𝐵1𝜎𝑥 = 75.129

𝛽1 = 𝑅𝑥𝑦 (𝜎𝑦𝜎𝑥) = 0.0079

SST = (n - 1) × Sy² = 1209026

SSR = r² × SST = 236200.2

MSR = SSR= 236200.2

SSE = SST - SSR = 972825.8

MSE = 𝑆𝑆𝐸

𝑛−2 = 6709.14

Syx = = 82

SSX = (n - 1) Sx ² = 5775936

Sb1 = = 0.04

t start = = 0.1975

➔ 𝑦 = 75.129 + 0.0079x

Conclusion: There is sufficient evidence that FPT stock trading volume affects the closing price of FPT stock As FPT stock trading volume increases, the closing price of FPT stock increases

V CONCLUSION

1 Summary of results

• Problem 1:

− With a 95% confidence interval, we can conclude that FPT's share price ratio above 75,000 VND is in the range of 86.567% to 95.746%

− With a 95% confidence interval, we can conclude that VNM's share price ratio above 75,000 VND is between 23.162% and 38.063%

• Problem 2:

− Based on the table => t-test > t-critical > - t-critical => Failed to reject H0 => It can

be confirmed that FPT's opening price difference VNM's opening price

− Based on the table => t-test > t-critical > - t-critical => Failed to reject H0 => It can

be confirmed that FPT's closing price difference VNM's closing price

• Problem 3:

This problem helps us to find a function that represents the relationship between FPT stock's trading volume and closing price of FPT stock The estimated regression line has formula: y=75.129+0.0079x

2 Restate the meaning of the project

The purpose of this project is to capture and compare the two values of two stocks, FPT and VNM, thereby answering concerns in investing in these two stocks

3 State skills learned through project work

− Review skills to calculate important statistics such as mean, standard deviation, Q1, Q2, Q3,

− Perfect skills such as: plotting summarizing data, finding confidence intervals, hypothesis testing and linear regression