Assessment Task – Tutorial Questions Assignment 2

Unit Code: HA1011

Unit Name: Applied Quantitative Methods

Assignment: Tutorial Questions Assignment 2

Due: 26th June 2020

Weighting: 25%

Total Marks: 50 Marks

Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in this unit

Unit Learning Outcomes Assessed:

1. Understand the pitfalls and benefits of statistics

2. Distinguish between the different survey sampling methods

3. Summarise numerical data and present it both by means of tables and charts

4. Be able to calculate and interpret descriptive summary measures

5. Develop simple regression models and interpret the regression coefficients

6. Understand basic probability concepts

7. Understand when to apply different distributions, their properties and how to calculate associated probabilities

8. Develop confidence interval estimates for the mean and the proportion

9. Perform Hypothesis Tests and interpret the results

Description

Each week students were provided with three tutorial questions of varying degrees of difficulty. These tutorial questions are available in the Tutorial Folder for each week on Blackboard. The Interactive Tutorials are designed to assist students with the process, skills and knowledge to answer the provided tutorial questions. Your task is to answer a selection of tutorial questions for weeks 7 to 11 inclusive and submit these answers in a single document.

Note:

You are NOT allowed to use Microsoft Excel for any calculations and you need to show all the steps in each question’s calculation. Students’ answers are not allowed to be 100% similar to any other student for any reason and this will NOT be tolerated. This MUST be your own work or penalties will apply! Refer to the section on “Academic Integrity” on page 3 of this document for more information.

The questions to be answered are:

Week 7 – Question 1 (10 marks)

a. Assume the online test in HA1011 has 15 multiple questions. Each question has five possible answers, of which only one is correct.

i. What is the probability that guesswork will yield at least seven correct answers? (2 marks) ii. What is the expected number of correct answers by guesswork? (2 marks)

b. At Delta limited the Chief Administrative Manager analyzed the number of incoming faxes. After an analysis, the manager determined the probability distribution of the number of pages per fax as follows:

x 1 2 3 4 5 6 7

P(x) 0.05 0.12 0.2 0.3 0.15 0.1 0.08

Required:

Compute the mean and the variance of the number of pages per fax. (6 marks)

Week 8 – Question 2 (10 marks)

An analysis of the amount of interest paid by ABX banks’ visa card holders reveals that the amount is normally distributed with a mean of $27 and a standard deviation of $7.

a. What proportion of the Bank’s Visa card holders pay more than $30 in interest? (2.5 marks)

b. What proportion of the Bank’s Visa card holders pay more than $40 in interest? (2.5 marks)

c. What proportion of the Bank’s Visa card holders pay less than $15 in interest? (2.5 marks)

d. What interest payment is exceeded by only 20% of the bank’s Visa cardholders? (2.5 marks)

Week 9 – Question 3 (10 marks)

a. Briefly discuss following 3 probability distributions

i. Uniform probability distribution

ii. Normal probability distribution

iii. Exponential probability distribution

(3 marks)

b. The amount of time that bankers devote to their job per week is normally distributed, with a mean of 52 hours and a standard deviation of 6 hours.

i. What is the probability that a banker works for more than 60 hours per week?

ii. Find the probability that the mean amount of work per week for 3 randomly selected bankers is more than 60 hours

iii. Find the probability that if three bankers are randomly selected, all three work for more than 60 hours per week (7 marks)

Week 10 – Question 4 (10 marks)

A researcher has collected a sample of 25 respondents and the mean was calculated as 500. The sample was randomly drawn from a normal population whose standard deviation is 15.

a) Estimate the population mean with 99% confidence (4 marks)

b) Repeat the part (a) changing the population standard deviation to 30. (2 marks)

c) Repeat the part (a) changing the population standard deviation to 60.

d) Describe what happens to the confidence interval estimate when the (2 marks)

standard deviation is increased. (2 marks)

Weeks 11 and 12 – Question 5 (10 marks)

The Coordinator of a Statistics unit has drawn a random sample of 12 undergraduates and asked how many hours they spent for studies. The average time of the selected sample was 34.25. The coordinator has recommended that students should spend 3 hours per week for 12 weeks semester, for a total of 36 hours. It is known that the population standard deviation is 8.

Based on the data listed below, using the p value approach, at 95% confidence level you are required to test whether there is evidence that the average student spent less than the recommended amount of time. You are required to arrange your answer based on the following steps:

a. State the hypotheses (2 marks)

b. Direction of the test (two tail/ left tail or right tail) (0.5 mark)

c. State the relevant test statistic and the reason for the selection (2 marks)

d. Level of significance (0.5 mark)

e. Decision rule (2 marks)

f. Calculate test statistics (2 marks)

g. Conclusion based on the above steps. (1 mark)

Submission Directions

The assignment has to be submitted via Blackboard. Each student will be permitted one submission to Blackboard only. Each student needs to ensure that the document submitted is the correct one.

Academic Integrity

Academic honesty is highly valued at Holmes Institute. Students must always submit work that represents their original words or ideas. If any words or ideas used in a class posting or assignment submission do not represent the student’s original words or ideas, the student must cite all relevant sources and make clear the extent to which such sources were used. Written assignments that include material similar to course reading materials or other sources should include a citation including source, author, and page number.

In addition, written assignments that are similar or identical to those of another student in the class is also a violation of the Holmes Institute’s Academic Conduct and Integrity Policy. The consequence for a violation of this policy can incur a range of penalties varying from a 50% penalty through to suspension of enrolment. The penalty would be dependent on the extent of academic misconduct and the student’s history of academic misconduct issues. All assessments will be automatically submitted to Safe-Assign to assess their originality.

Further Information:

For further information and additional learning resources, students should refer to their Discussion Board for the unit.

Unit Code: HA1011

Unit Name: Applied Quantitative Methods

Assignment: Tutorial Questions Assignment 2

Due: 26th June 2020

Weighting: 25%

Total Marks: 50 Marks

Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in this unit

Unit Learning Outcomes Assessed:

1. Understand the pitfalls and benefits of statistics

2. Distinguish between the different survey sampling methods

3. Summarise numerical data and present it both by means of tables and charts

4. Be able to calculate and interpret descriptive summary measures

5. Develop simple regression models and interpret the regression coefficients

6. Understand basic probability concepts

7. Understand when to apply different distributions, their properties and how to calculate associated probabilities

8. Develop confidence interval estimates for the mean and the proportion

9. Perform Hypothesis Tests and interpret the results

Description

Each week students were provided with three tutorial questions of varying degrees of difficulty. These tutorial questions are available in the Tutorial Folder for each week on Blackboard. The Interactive Tutorials are designed to assist students with the process, skills and knowledge to answer the provided tutorial questions. Your task is to answer a selection of tutorial questions for weeks 7 to 11 inclusive and submit these answers in a single document.

Note:

You are NOT allowed to use Microsoft Excel for any calculations and you need to show all the steps in each question’s calculation. Students’ answers are not allowed to be 100% similar to any other student for any reason and this will NOT be tolerated. This MUST be your own work or penalties will apply! Refer to the section on “Academic Integrity” on page 3 of this document for more information.

The questions to be answered are:

Week 7 – Question 1 (10 marks)

a. Assume the online test in HA1011 has 15 multiple questions. Each question has five possible answers, of which only one is correct.

i. What is the probability that guesswork will yield at least seven correct answers? (2 marks) ii. What is the expected number of correct answers by guesswork? (2 marks)

b. At Delta limited the Chief Administrative Manager analyzed the number of incoming faxes. After an analysis, the manager determined the probability distribution of the number of pages per fax as follows:

x 1 2 3 4 5 6 7

P(x) 0.05 0.12 0.2 0.3 0.15 0.1 0.08

Required:

Compute the mean and the variance of the number of pages per fax. (6 marks)

Week 8 – Question 2 (10 marks)

An analysis of the amount of interest paid by ABX banks’ visa card holders reveals that the amount is normally distributed with a mean of $27 and a standard deviation of $7.

a. What proportion of the Bank’s Visa card holders pay more than $30 in interest? (2.5 marks)

b. What proportion of the Bank’s Visa card holders pay more than $40 in interest? (2.5 marks)

c. What proportion of the Bank’s Visa card holders pay less than $15 in interest? (2.5 marks)

d. What interest payment is exceeded by only 20% of the bank’s Visa cardholders? (2.5 marks)

Week 9 – Question 3 (10 marks)

a. Briefly discuss following 3 probability distributions

i. Uniform probability distribution

ii. Normal probability distribution

iii. Exponential probability distribution

(3 marks)

b. The amount of time that bankers devote to their job per week is normally distributed, with a mean of 52 hours and a standard deviation of 6 hours.

i. What is the probability that a banker works for more than 60 hours per week?

ii. Find the probability that the mean amount of work per week for 3 randomly selected bankers is more than 60 hours

iii. Find the probability that if three bankers are randomly selected, all three work for more than 60 hours per week (7 marks)

Week 10 – Question 4 (10 marks)

A researcher has collected a sample of 25 respondents and the mean was calculated as 500. The sample was randomly drawn from a normal population whose standard deviation is 15.

a) Estimate the population mean with 99% confidence (4 marks)

b) Repeat the part (a) changing the population standard deviation to 30. (2 marks)

c) Repeat the part (a) changing the population standard deviation to 60.

d) Describe what happens to the confidence interval estimate when the (2 marks)

standard deviation is increased. (2 marks)

Weeks 11 and 12 – Question 5 (10 marks)

The Coordinator of a Statistics unit has drawn a random sample of 12 undergraduates and asked how many hours they spent for studies. The average time of the selected sample was 34.25. The coordinator has recommended that students should spend 3 hours per week for 12 weeks semester, for a total of 36 hours. It is known that the population standard deviation is 8.

Based on the data listed below, using the p value approach, at 95% confidence level you are required to test whether there is evidence that the average student spent less than the recommended amount of time. You are required to arrange your answer based on the following steps:

a. State the hypotheses (2 marks)

b. Direction of the test (two tail/ left tail or right tail) (0.5 mark)

c. State the relevant test statistic and the reason for the selection (2 marks)

d. Level of significance (0.5 mark)

e. Decision rule (2 marks)

f. Calculate test statistics (2 marks)

g. Conclusion based on the above steps. (1 mark)

Submission Directions

The assignment has to be submitted via Blackboard. Each student will be permitted one submission to Blackboard only. Each student needs to ensure that the document submitted is the correct one.

Academic Integrity

Academic honesty is highly valued at Holmes Institute. Students must always submit work that represents their original words or ideas. If any words or ideas used in a class posting or assignment submission do not represent the student’s original words or ideas, the student must cite all relevant sources and make clear the extent to which such sources were used. Written assignments that include material similar to course reading materials or other sources should include a citation including source, author, and page number.

In addition, written assignments that are similar or identical to those of another student in the class is also a violation of the Holmes Institute’s Academic Conduct and Integrity Policy. The consequence for a violation of this policy can incur a range of penalties varying from a 50% penalty through to suspension of enrolment. The penalty would be dependent on the extent of academic misconduct and the student’s history of academic misconduct issues. All assessments will be automatically submitted to Safe-Assign to assess their originality.

Further Information:

For further information and additional learning resources, students should refer to their Discussion Board for the unit.

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