Student Number: (enter on the line below)

Student Name: (enter on the line below)

HA1011

Applied quantitative methods

final assessmeNt

Trimester t 1, 2021

Assessment Weight: 50 total marks

Instructions:

All questions must be answered by using the answer boxes provided in this paper.

Completed answers must be submitted to Blackboard by the published due date and time.

Submission instructions are at the end of this paper.

Purpose:

This assessment consists of six (6) questions and is designed to assess your level of knowledge of the key topics covered in this unit

Question 1 ( 7marks)

Use the following sample data to calculate the following summary statistics

X Y

5 20

7 50

4 10

5 20

5 30

5 20

3 10

8 50

2 10

2 5

A.Calculate the mean for X and Y (1 marks)

ANSWER: ** Answer box will enlarge as you type

B.Calculate the standard deviation for X and Y (3 marks)

ANSWER: ** Answer box will enlarge as you type

C.Calculate the correlation coefficient (r) Using formula (3 marks)

ANSWER: ** Answer box will enlarge as you type

Question 2 ( 7 marks)

The study on Price ($) and Sales of automobiles resulted in the following data: Use the following formula to calculate the correlation r between the Sakes (Y) and the price (X) in the table below:

Price (X) 10 20 30 40 50 60 70 80 90 100

Sales (Y) 28 25 25 19 15 12 9 10 6 5

Use the variables and numbers in the table above to calculate the equation of the regression line:

y is the predicted value of y (Sales) using x (Cost) with bo (the sample intercept) and b1 (the sample slope).

A. Calculate b1 (3 marks)

ANSWER:

B. Calculate b0 (1 marks)

ANSWER:

C. Write the equation of the regression line (1 mark):

ANSWER:

D. What is the estimated value, y for x = 15? (2 marks)

ANSWER:

Question 3 ( 7marks)

Unemployment rate in a certain city stands at 30%. If a random sample of 10 residents in this city is selected. 7 marks

Required:

A.What is the probability that we get one unemployed person? (2 marks)

ANSWER:

B.What is the probability that we get at most two unemployed residents? (3 marks)

ANSWER:

C.Find the mean and variance. (2 marks)

ANSWER:

Question 4 (7 marks)

The daily demand for rice at a shopping center is normally distributed with a mean of 2100 kg and a standard deviation of 200 kg. In the morning, the manager found that there are only 1800 kg of rice available.

A,What is the probability that the shopping center will run out for rice before closing on that day? (3 marks)

ANSWER:

B.What is the probability that there will be demand of rice in between 2000 kg and 2200 kg? (4marks)

ANSWER:

Question 5 (11 marks)

Sales personnel for a product distributor submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2.

A.Find a 90% confidence interval for the population mean and interpret. (5 Marks)

ANSWER:

B.Find a 95% confidence interval for the population mean and interpret. (5 Marks)

ANSWER:

C.Compare the intervals between 90% and 95% confidence level. (1 Mark)

ANSWER:

Question 6 (marks)

A. A sample of 25 items produced a mean of 46. Assume that the population standard deviation is 6 and test the following hypothesis with a = 0.05 (6 Marks)

Ho: µ = 50

H1: µ 50

ANSWER:

B. A sample of 25 students revealed that the average age of students at Holmes is 21 years and the standard deviation of age is 1.8. Test the hypothesis that the population mean of the student age is greater than 19 at 10% significance level. (5 Marks)

ANSWER:

END OF FINAL ASSESSMENT

Submission instructions:

Save submission with your STUDENT ID NUMBER and UNIT CODE e.g EMV54897 HA1011

Submission must be in MICROSOFT WORD FORMAT ONLY

Upload your submission to the appropriate link on Blackboard

Only one submission is accepted. Please ensure your submission is the correct document.

All submissions are automatically passed through SafeAssign to assess academic integrity.

Student Name: (enter on the line below)

HA1011

Applied quantitative methods

final assessmeNt

Trimester t 1, 2021

Assessment Weight: 50 total marks

Instructions:

All questions must be answered by using the answer boxes provided in this paper.

Completed answers must be submitted to Blackboard by the published due date and time.

Submission instructions are at the end of this paper.

Purpose:

This assessment consists of six (6) questions and is designed to assess your level of knowledge of the key topics covered in this unit

Question 1 ( 7marks)

Use the following sample data to calculate the following summary statistics

X Y

5 20

7 50

4 10

5 20

5 30

5 20

3 10

8 50

2 10

2 5

A.Calculate the mean for X and Y (1 marks)

ANSWER: ** Answer box will enlarge as you type

B.Calculate the standard deviation for X and Y (3 marks)

ANSWER: ** Answer box will enlarge as you type

C.Calculate the correlation coefficient (r) Using formula (3 marks)

ANSWER: ** Answer box will enlarge as you type

Question 2 ( 7 marks)

The study on Price ($) and Sales of automobiles resulted in the following data: Use the following formula to calculate the correlation r between the Sakes (Y) and the price (X) in the table below:

Price (X) 10 20 30 40 50 60 70 80 90 100

Sales (Y) 28 25 25 19 15 12 9 10 6 5

Use the variables and numbers in the table above to calculate the equation of the regression line:

y is the predicted value of y (Sales) using x (Cost) with bo (the sample intercept) and b1 (the sample slope).

A. Calculate b1 (3 marks)

ANSWER:

B. Calculate b0 (1 marks)

ANSWER:

C. Write the equation of the regression line (1 mark):

ANSWER:

D. What is the estimated value, y for x = 15? (2 marks)

ANSWER:

Question 3 ( 7marks)

Unemployment rate in a certain city stands at 30%. If a random sample of 10 residents in this city is selected. 7 marks

Required:

A.What is the probability that we get one unemployed person? (2 marks)

ANSWER:

B.What is the probability that we get at most two unemployed residents? (3 marks)

ANSWER:

C.Find the mean and variance. (2 marks)

ANSWER:

Question 4 (7 marks)

The daily demand for rice at a shopping center is normally distributed with a mean of 2100 kg and a standard deviation of 200 kg. In the morning, the manager found that there are only 1800 kg of rice available.

A,What is the probability that the shopping center will run out for rice before closing on that day? (3 marks)

ANSWER:

B.What is the probability that there will be demand of rice in between 2000 kg and 2200 kg? (4marks)

ANSWER:

Question 5 (11 marks)

Sales personnel for a product distributor submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2.

A.Find a 90% confidence interval for the population mean and interpret. (5 Marks)

ANSWER:

B.Find a 95% confidence interval for the population mean and interpret. (5 Marks)

ANSWER:

C.Compare the intervals between 90% and 95% confidence level. (1 Mark)

ANSWER:

Question 6 (marks)

A. A sample of 25 items produced a mean of 46. Assume that the population standard deviation is 6 and test the following hypothesis with a = 0.05 (6 Marks)

Ho: µ = 50

H1: µ 50

ANSWER:

B. A sample of 25 students revealed that the average age of students at Holmes is 21 years and the standard deviation of age is 1.8. Test the hypothesis that the population mean of the student age is greater than 19 at 10% significance level. (5 Marks)

ANSWER:

END OF FINAL ASSESSMENT

Submission instructions:

Save submission with your STUDENT ID NUMBER and UNIT CODE e.g EMV54897 HA1011

Submission must be in MICROSOFT WORD FORMAT ONLY

Upload your submission to the appropriate link on Blackboard

Only one submission is accepted. Please ensure your submission is the correct document.

All submissions are automatically passed through SafeAssign to assess academic integrity.

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