ECO502 Decision Making

Semester 1, 2016

Assignment 2

Maximum marks: 30

Answer all Questions

Due date: 0900 Tuesday May 3, 2016 (week 9)

Question 1

The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60.

a) Applicants need a test score higher than 530 to be admitted into the graduate program. What proportion of applications qualify?

[Marks 2]

b) If the university wishes to set the cutoff score for graduate admission so that only the top 10% of applicants qualify for admission, what is the required cutoff score?

[Marks 2]

c) What percentage of applicants have test scores within two standard deviations of the mean?

[Marks 3]

Question 2

Government officials in Canberra have recently expressed concern regarding overruns on military contracts. These unplanned expenditures have been costing Australians millions of dollars every year. The prime minister impanels a committee of experts to estimate the average amount each contract costs the government over and above the amount agreed upon. The committee has already determined that the standard deviation in overruns is $17.5 million, and that they appear normally distributed.

i. If a sample of 25 contracts is selected, how likely is it the sample will overestimate the population mean by more than $10 million?

[Marks 3]

ii. The prime minister will accept an error of $5 million in the estimate of µ. How likely is he to receive an estimate from the committee within the specified range?

[Marks 4]

Question 3

a) You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the mean time required to complete a particular unit of the manufacturing process. A sample of 600 units yields a mean of 7.2 days. Since the population standard deviation is unknown, the sample standard deviation of s=1.9 days must be used. Calculate and interpret the 90 percent interval for the mean completion time for the manufacturing process. If this mean time is estimated to be in excess of 7 days, a new process will be implemented to reduce production costs.

[Marks 4]

b) A construction firm was charged with inflating the expense vouchers it files for construction contracts with the federal government. The contract states that a certain type of job should average $1,150. In the interest of time, the directors of only 12 government agencies were called on to enter court testimony regarding the firm’s vouchers. If a mean of $1,275 and a standard deviation of $235 are discovered from testimony, would a 95 percent confidence interval support the firm’s legal case? Assume voucher amounts are normal.

[Marks 4]

Question 4

a) The mean size of commercial loans by a bank has been $60,000 in the past. A recent change in the bank’s credit policy allows larger amounts to be borrowed under the same terms. The credit manager now wishes to test whether the mean size of commercial loans made since the policy changes is larger than $60,000. The manager wishes to control the a risk at 0.01 when µ=$60,000. A random sample of n=144 loans made since the policy change yielded the following results =$68,100, s=$45,000.

i. Conduct the test. State the alternatives, the decision rule, the value standardised test statistic and the conclusion.

[Marks 4]

ii. Calculate the p-value of the test and conduct the required test. Interpret its meaning here.

[Marks 4]

*****The End*****

Semester 1, 2016

Assignment 2

Maximum marks: 30

Answer all Questions

Due date: 0900 Tuesday May 3, 2016 (week 9)

Question 1

The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60.

a) Applicants need a test score higher than 530 to be admitted into the graduate program. What proportion of applications qualify?

[Marks 2]

b) If the university wishes to set the cutoff score for graduate admission so that only the top 10% of applicants qualify for admission, what is the required cutoff score?

[Marks 2]

c) What percentage of applicants have test scores within two standard deviations of the mean?

[Marks 3]

Question 2

Government officials in Canberra have recently expressed concern regarding overruns on military contracts. These unplanned expenditures have been costing Australians millions of dollars every year. The prime minister impanels a committee of experts to estimate the average amount each contract costs the government over and above the amount agreed upon. The committee has already determined that the standard deviation in overruns is $17.5 million, and that they appear normally distributed.

i. If a sample of 25 contracts is selected, how likely is it the sample will overestimate the population mean by more than $10 million?

[Marks 3]

ii. The prime minister will accept an error of $5 million in the estimate of µ. How likely is he to receive an estimate from the committee within the specified range?

[Marks 4]

Question 3

a) You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the mean time required to complete a particular unit of the manufacturing process. A sample of 600 units yields a mean of 7.2 days. Since the population standard deviation is unknown, the sample standard deviation of s=1.9 days must be used. Calculate and interpret the 90 percent interval for the mean completion time for the manufacturing process. If this mean time is estimated to be in excess of 7 days, a new process will be implemented to reduce production costs.

[Marks 4]

b) A construction firm was charged with inflating the expense vouchers it files for construction contracts with the federal government. The contract states that a certain type of job should average $1,150. In the interest of time, the directors of only 12 government agencies were called on to enter court testimony regarding the firm’s vouchers. If a mean of $1,275 and a standard deviation of $235 are discovered from testimony, would a 95 percent confidence interval support the firm’s legal case? Assume voucher amounts are normal.

[Marks 4]

Question 4

a) The mean size of commercial loans by a bank has been $60,000 in the past. A recent change in the bank’s credit policy allows larger amounts to be borrowed under the same terms. The credit manager now wishes to test whether the mean size of commercial loans made since the policy changes is larger than $60,000. The manager wishes to control the a risk at 0.01 when µ=$60,000. A random sample of n=144 loans made since the policy change yielded the following results =$68,100, s=$45,000.

i. Conduct the test. State the alternatives, the decision rule, the value standardised test statistic and the conclusion.

[Marks 4]

ii. Calculate the p-value of the test and conduct the required test. Interpret its meaning here.

[Marks 4]

*****The End*****

The Assignment 3 Specification and Marking CriteriaSome Theoretical Issues in Distributed SystemsIn this assignment, you are to address some theoretical issues in the area of distributed systems or distributed...Project Specification301116 Social Media IntelligenceDue Date: Friday of Week 10AimThe Project requires us to analyse social media data using the knowledge obtained from this unit with assistance from...Assignment brief, FAQs & rubric for Assessment 3 Communicating Health and Science 54090 Autumn 2019 v1Assessment requirements and FAQsAssessment task 3: Communication portfolio & reflectionWeight:...Kindly follow all the details mentioned in word file.Assignment 1 CST3009Due date: 20 Jun,2020Weighting: 20%ReportAs part of the restructure of management of the business process the management of ABC...Assessment Task 1 Information: Reflective Thinking TaskYou have been asked to observe where critical and creative skills are utilised in the workplace, then to reflect on the situation, the people and...ITSA2005Planning and Implementing ServerAssignmentAssignment Type Group Assignment (4 students in each group)Week Issued 5Total Marks 100Weight 20%Submission Deadline Week 12 via MoodleSubmission files...COMP2741/8714: Application DevelopmentAssignment 2: GUI Implementation and Testing YouTube TrenderSubmission Date Midnight, Wednesday, Week 14Important InformationYou do NOT need a YouTube/Google account...**Show All Questions**