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DEC215 Business Statistics

Dr. A. Ampountolas Fall22

Assignment sheet 3

Due date: 11.12.2022 @ 11:59pm

Exercise 1.

The National Insurance Crime Bureau says that Miami- Dade, Broward, and palm

Beach counties account for a substantial number of questionable insurance claims

referred to investigators. Assume that the number of questionable insurance claims

referred to investigators by Miami-Dade, Broward, and Palm Beach counties is

distributed as a Poisson random variable with a mean of 10 per day.

Questions:

1. What assumptions need to be made so that the number of questionable insurance

claims referred to investigators by Miami- Dade, Broward, and Palm Beach

counties is distributed as a Poisson random variable?

Making the assumptions given in (1), what is the probability that:

2. 5 questionable insurance claims will be referred to investigators by Miami-Dade,

Broward, and Palm Beach counties in a day?

3. 10 or fewer questionable insurance claims will be referred to investigators by

Miami-Dade, Broward, and Palm Beach counties in a day?

4. 11 or more questionable insurance claims will be referred to investigators by

Miami-Dade, Broward, and Palm Beach counties in a day?

Exercise 2.

Spurious correlation refers to the apparent relationship between variables that either

has no true relationship or are re-related to other variables that have not been

measured. One widely publicized stock market indicator in the United States that is an

example of spurious correlation is the relationship between the National Football

League Super Bowl winner and the per- performance of the Dow Jones Industrial

Average in that year. The indicator states that when a team that existed before the

National Football League merged with the American Football League wins the Super

Bowl, the Dow Jones Industrial Average will increase in that year. Since the first Super

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Bowl was held in 1967 through 2012, the indicator has been correct 37 out of 46 times.

Assuming that this indicator is a random event with no predictive value, you would

expect that the indicator would be correct 50% of the time.

Questions:

1. What is the probability that the indicator would be correct 37 or more times in 46

years?

2. What does this tell you about the usefulness of this indicator?

Exercise 3.

In the Florida lottery Lotto game, you select six numbers from a pool of numbers from

1 to 53. each wager costs $1. You win the jackpot if you match all six numbers that you

have selected.

Questions:

Find the probability of:

1. winning the jackpot.

2. matching five numbers.

3. matching four numbers.

4. matching three numbers.

5. matching two numbers.

6. matching one number.

7. matching none of the numbers.

8. If you match zero, one, or two numbers, you do not win anything. What is the

probability that you will not win anything?

9. The Lotto ticket gives complete game rules and probabilities of matching zero

through six numbers. The lottery ticket has the saying ”A Win for education” on

the back of the ticket. Do you think Florida’s slogan and the printed complete

game rules and probabilities of matching zero through six numbers is an ethical

approach to running the lottery game?

Exercise 4.

The Consumer Financial Protection Bureaus consumer response team hears directly

from consumers about the challenges they face in the marketplace, brings their concerns

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to the attention of financial institutions, and assists in addressing their complaints.

Consumer response accepts complaints related to mortgages, bank accounts and

services, private student loans, other consumer loans, and credit reporting. Of the

consumers who registered a bank account and service complaint, 41% cited ”account

management” as the type of complaint; these complaints are related to opening, closing,

or managing the account and addressing issues, such as confusing marketing, denial,

fees, statements, and joint accounts. Consider a sample of 20 consumers who registered

bank accounts and service complaints. Use the binomial model to answer the following

questions:

Questions:

1. What is the expected value, or mean, of the binomial distribution?

2. What is the standard deviation of the binomial distribution?

3. What is the probability that 10 of the 20 consumers cited ”account management”

as the type of complaint?

4. What is the probability that no more than 5 of the consumers cited ”account

management” as the type of complaint?

5. What is the probability that 5 or more of the consumers cited ”account

management” as the type of complaint?

Exercise 5.

Zagat’s publishes restaurant ratings for various locations in the United States. the file

restaurants contain the Zagat rating for food, decor, service, and the cost per person for

a sample of 100 restaurants located in New York City and in a suburb of New York

City. Develop a regression model to predict the cost per person based on a variable that

represents the sum of the ratings for food, decor, and service (use the enclosed excel file:

NYC Restaurants.xlsx).

Questions:

1. Construct a scatter plot.

2. Assuming a linear relationship, use the simple linear regression method to

compute the regression coefficients b0 and b1.

3. Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem.

4. Predict the mean cost per person for a restaurant with a summated rating of 50.

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5. What should you tell the owner of a group of restaurants in this geographical area

about the relationship between the summated rating and the cost of a meal?

Exercise 6.

Measuring the height of a California redwood tree is very difficult because these trees

grow to heights over 300 feet. People familiar with these trees understand that the

height of a California redwood tree is related to other characteristics of the tree,

including the diameter of the tree at the breast height of a person (in inches) and the

thickness of the bark of the tree (in inches). The excel file Redwood.xlsx contains the

height, diameter at breast height of a person, and bark thickness for a sample of 21

California redwood trees.

Questions:

1. Use the multiple regression method to compute the regression coefficients.

2. State the multiple regression equation that predicts the height of a tree based on

the tree’s diameter at breast height and the thickness of the bark.

3. Interpret the meaning of the slopes in this equation.

4. Predict the mean height for a tree that has a breast height diameter of 25 inches

and a bark thickness of 2 inches.

5. Interpret the meaning of the coefficient of multiple determination in this problem.

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Thank you!

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