STATISTICAL ANALYSIS (MAT10251)

ASSESSMENT 2 – CALCULATIONS AND SHORT WRITTEN RESPONSES (30%)

INSTRUCTIONS

Perform and show the required calculations, present your findings, and prepare short written responses to the following questions. Please submit your answers in a single file.

Question 1 - Basic Probability (10 marks)

According to a recent study, 9 out of 10 parents have helped their adult children with some financial assistance. The following table shows the number of times parents have given their adult children financial assistance to buy a car and to pay the rent.

Pay the rent

Yes No

Buy a car Yes 90 50

No 10 150

a. Develop a joint probability table. (2 marks)

b. Using the marginal probabilities for ‘buy a car’ and ‘pay the rent’, are parents more likely to assist their adult children with buying a car or paying the rent? What is your interpretation of the marginal probabilities? (2 marks)

c. If parents provided financial assistance to buy a car, what is the probability that the parents assisted with paying rent? (2 marks)

d. If parents did not provide financial assistance to buy a car, what is the probability that the parents assisted with paying rent? (2 marks)

e. What is the probability that parents provided financial assistance for their adult children by either helping to buy a car or pay rent? (2 marks)

Question 2 – Normal Distribution (10 marks)

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 160 minutes and a standard deviation of 20 minutes. Answer the following questions:

a. What is the probability of completing the exam in 120 minutes or less? (2 marks)

b. What is the probability that a student will complete the exam in more than 120 minutes but less than 150 minutes? (2 marks)

c. What is the probability that a student will complete the exam in more than 100 minutes but less than 170 minutes? (2 marks)

d. Assume that the class has 120 students and that the examination period is 180 minutes in length. How many students do you expect will be unable to complete the examination in the allotted time? (4 marks)

1

Question 3 – Sampling Distribution (10 marks)

The Economics Policy Institute periodically issues reports on wages of entry-level workers. The Institute reported that entry-level wages for male college graduates were $43.36 per hour, and for female college graduates were $37.60 per hour. Assume the standard deviation for male graduates is $2.30 and for female graduates is $2.05.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $0.50 of the population mean, $43.36? (3 marks)

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $0.50 of the population mean, $37.60? (3 marks)

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $0.50 of the population mean? Why? (2 marks)

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $0.30 below the population mean? (2 marks)

2

ASSESSMENT 2 – CALCULATIONS AND SHORT WRITTEN RESPONSES (30%)

INSTRUCTIONS

Perform and show the required calculations, present your findings, and prepare short written responses to the following questions. Please submit your answers in a single file.

Question 1 - Basic Probability (10 marks)

According to a recent study, 9 out of 10 parents have helped their adult children with some financial assistance. The following table shows the number of times parents have given their adult children financial assistance to buy a car and to pay the rent.

Pay the rent

Yes No

Buy a car Yes 90 50

No 10 150

a. Develop a joint probability table. (2 marks)

b. Using the marginal probabilities for ‘buy a car’ and ‘pay the rent’, are parents more likely to assist their adult children with buying a car or paying the rent? What is your interpretation of the marginal probabilities? (2 marks)

c. If parents provided financial assistance to buy a car, what is the probability that the parents assisted with paying rent? (2 marks)

d. If parents did not provide financial assistance to buy a car, what is the probability that the parents assisted with paying rent? (2 marks)

e. What is the probability that parents provided financial assistance for their adult children by either helping to buy a car or pay rent? (2 marks)

Question 2 – Normal Distribution (10 marks)

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 160 minutes and a standard deviation of 20 minutes. Answer the following questions:

a. What is the probability of completing the exam in 120 minutes or less? (2 marks)

b. What is the probability that a student will complete the exam in more than 120 minutes but less than 150 minutes? (2 marks)

c. What is the probability that a student will complete the exam in more than 100 minutes but less than 170 minutes? (2 marks)

d. Assume that the class has 120 students and that the examination period is 180 minutes in length. How many students do you expect will be unable to complete the examination in the allotted time? (4 marks)

1

Question 3 – Sampling Distribution (10 marks)

The Economics Policy Institute periodically issues reports on wages of entry-level workers. The Institute reported that entry-level wages for male college graduates were $43.36 per hour, and for female college graduates were $37.60 per hour. Assume the standard deviation for male graduates is $2.30 and for female graduates is $2.05.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $0.50 of the population mean, $43.36? (3 marks)

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $0.50 of the population mean, $37.60? (3 marks)

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $0.50 of the population mean? Why? (2 marks)

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $0.30 below the population mean? (2 marks)

2

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