Analyze the probability of given business outcomes using fundamental probability concepts for discrete and continuous probability distributions.

INTRODUCTION:

Statistics is a branch of mathematics, which involves:
1. Collecting data.
2. Organizing and analyzing data.
3. Drawing conclusions from data.

OBJECTIVE:

This case study is designed to develop students’ ability to assess and critically interpret statistics and business
information and apply them in changing business environments.
Assessment Learning Outcomes:

LO1- Discrete and Continuous Probability Distributions (Chapters 5, 6, 7).

Analyze the probability of given business outcomes using fundamental probability concepts for discrete and continuous probability distributions.

LO2-Sampling Methods and Central Limit Theorem (Chapter 8).

Apply concepts of sampling and the Central Limit Theorem in obtaining information that will facilitate the analysis of appropriate business issues.

LO3- Estimation and Confidence Intervals (Chapter 9).

Compute probability of given business outcomes by building one and two tailed confidence intervals for

Z and t probability distributions.
LO4, 5- One-Sample Tests of Hypothesis (Chapter 10).

Test different business hypothesis by applying the concepts of confidence intervals, test statistics, p-value, type I and II errors, sample sizes and finite populations. Draw statistical inferences from given business information, based on one and two tailed hypothesis tests.
LO6: Correlation and Linear Regression (Chapter 13).

Assess the likely relationships between dependent and independent variables in business situations using correlation and regression techniques.

Due Date:

The hard and soft copy of the project
The individual presentation of the project
Marking Allocation:
The project marks are allocated on a group and individual basis. Group marks are allocated based on correctly answering the questions set in the project and how, as a group the results and how clearly the data is presented.

Individuals will be graded based upon their contribution to the presentation, explanation and understanding of the data and how they answer questions directed to them during the presentation.
Marking split:
• Group: 80 %
• Individual: 20 %

Marks
Allocated 8 16 14 10 8 14 10 80 20 100
Marks
Obtained

Declaration:

 No part of this assignment has been copied from another source, (not from another group or student, an internet source or a book.
 No part of this assignment has been written for me by any other person.

Name ID Signature
1.
2.
3.
4.
5.

OVERVIEW:

Referring to the Real Estate sales data, which reports information on 60 homes sold in Al Reem Island area during the last year, there are many factors that can affect the selling price of homes such as the location, the number of bedrooms, number of bathrooms, the size of a home in a square feet, whether there is a pool or not, and whether there is a garage or not.
The main purpose of this study is to test if there is a relationship between Real estate sales prices and the above mentioned factors that seem to affect homes prices.
STEPS:

1) The data will be distributed to the students, each group will have a different data set as follows:

No. Price in
AED
Size of a home in square feet No. of Rooms No of bathrooms
Garage
Pool Distance Location
Key points to follow:

• Selling price in AED, the current price of the home evaluated by a professional.
• Size of the home in square feet: the total area of the house (including the garage, pool, etc.)
• Number of bedrooms: the no. of rooms in the house.
• No. of bathrooms: the no. of bathrooms in the house.
• Garage: 1 if the house has garage .zero if not. (1 = yes, 0 = no)
• Pool: 1 if the house has pool .zero if not. (1 = yes, 0 = no)
• Distance: the distance in Km between the HCT ADWC campus and the house.
• Location: the region in which the house is located
o 1: Abu Dhabi City
o 2: Khalifa city
o 3.Shahama
o 4.Bani Yas
o 5.Bahia
Refer to the data given by your teacher complete the following tasks.
TASK 1 – Chapter 5 (A Survey of Probability Concepts)

Construct a contingency table as given below to answer the following questions: 2 marks
Location
1(AD) 2(Khalifa) 3(Shahama) 4(Bani Yas) 5(Bahia)
Has Garage
Has No Garage

1. What approach of probability did you use? 1 mark
2. What is the probability of selecting a home with Garage? 1 mark
3. Find the probability of selecting a home in Bani Yas? 1 mark
4. Calculate the probability of selecting a home in Khalifa and has Garage? 1 mark
5. What is the probability of selecting a home in Bahia or has No Garage? 2marks
TASK 2-A – Chapter 6 (Probability Distribution)

1. Use column “number of bedrooms” to create a probability distribution. 2marks
2. Use your probability distribution to find the probability of selecting a home with more than 3
Bedrooms. 1 mark
3. Using the probability distribution table find the expected number of bedrooms. 2marks
4. Find the variance using the probability distribution. 2marks
TASK 2-B – Chapter 6 (Binomial Distribution)

5. Using MegaStat create a binomial distribution with n=60, p= probability of selecting a home with a pool and explain what does the chart show? 2marks
6. What are the expected number and the standard deviation of selecting a home with a pool? 2marks
7. What is the probability that all homes have a pool? 1mark
8. What is the percentage that fewer than 15 homes have a pool? 2marks
9. What is the probability that between 23 and 31 homes have a pool? 2marks
TASK 3: Chapter 7 (Continuous Probability Distributions)

1. Compute the mean and the standard deviation of the sales prices of the 60 homes. 2marks
2. What is the probability that the area of the house would be no more than 2,000 square feet? 2marks
3. What is the probability that the area of the house would be at least 2,100 square feet? 2marks
4. What is the probability that the area of the house would be between 2,200 square feet and 2,500 square feet? 2marks
5. About 68% of the areas of the houses fall between what two values? (Use Empirical rule) 2marks
6. Between what two area values does the middle 75% of homes (60 homes) fall? 2marks
7. What is the area of a house that separates the top 20% from the lower 80% of the 60 homes? 2marks

TASK 4: Chapter 8 (Sampling Methods)

1. Select a sample A of 16 homes from the 60 homes dataset then paste it into a new sheet and name it as (Sample A).

Use systematic method and mention the system that you have used. 2 marks
2. Select a sample B of 36 homes from the 60 homes dataset then paste it in a new sheet and name it as (Sample B). Use cluster method and explain. 2 marks
3. Compute the mean, the standard deviation and the standard error of the home prices of sample A. 2 marks
4. Compute the mean, the standard deviation and the standard error of the home prices of sample B. 1 mark
5. Compare answer 4) and 5). How can the sample error be reduced? 1 mark
6. What is the probability that the home prices of sample A would be less than AED 2,500,000? 2marks
TASK 5: Chapter 9 (Estimation and Confidence Intervals)

1. Compute the mean (µ) and the standard deviation (σ) of the home prices of your dataset

(60 homes). 1mark
2. For sample A, compute the mean and the standard deviation of home prices for the 16
homes
3. For sample B, compute the mean and the standard deviation of the home prices for the 36 homes

4. For Sample A, what is the point estimate of the population mean of the homes prices? 1mark

5. The Government in Abu Dhabi wish to have information on the mean homes’ prices. Assume that the population standard deviation is AED 470,000.
By using Sample A, what is a reasonable range of values for the population mean? (Use 95%
confidence level). Use mean: ̅A and =470,000
Would it be reasonable to conclude that the population homes’ prices mean is AED 2,000,000? 2marks
6. Assume that is unknown. By using Sample B, construct a 90 percent confidence interval for the population mean. [Use the mean and the standard deviation of Sample B]
Would it be reasonable to conclude that the population homes’ prices mean is AED 2,800,000? 2marks
7. How large a sample is needed to find the populations mean of the homes prices within AED 150,000 at 99 percent confidence? Use the standard deviation of your population (60 homes). 2marks
TASK 6: Chapter 10 (One-Sample Tests of Hypothesis).

1. A researcher claims that the prices of homes in Abu Dhabi are less than AED 2,500,000. Use your dataset of 60 homes, and a population standard deviation of UAE is AED 470,000.
Is there evidence to support the claim at a 0.05? Use the traditional method. Show all the steps. 6 marks
2. A researcher claims that the home prices in Abu Dhabi are AED 3,000,000. By using Sample
B and assuming that is unknown [Use the mean and the standard deviation of Sample B] ;
test the claim at
a) 0.01 significance level
b) 0.05 significance level
Use the P-value method. Show all the steps. 8 marks

TASK 7: Chapter 13 (Correlation and Linear Regression)
QUESTION TO ANSWER: Are the home price and the distance away from the city related?
1. Determine the dependent variable and the independent variable. Describe the relationship
between the dependent variable and the independent variable. Draw the scatter diagram of your dataset (60 homes). 2marks
2. Determine the regression equation. What is a regression equation and what is it used for? 2marks
3. What is the slope of the regression line? What does it represent? 1 mark
4. State the value of Y- intercept. Comment on its value. 1 mark
5. State the value of correlation coefficient. Comment on its value. 1 mark
6. State the value of coefficient of determination. Comment on its value. 1 mark
7. Predict the selling price of a home 23 kilometers from the center of the city. Comment on the reliability of your prediction.

1 mark
8. Estimate the distance of a home whose price is AED 2,900,000. Comment on your estimation. 1 mark

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