CALCULATION IN STATISTICS

STATS6900 Quantitative Methods for Business

Assignment – Semester 1, 2012

Date Due:        Refer to Unit Description

Total Marks:   45 marks                                              Worth:  20% of final assessment

This assignment requires a considerable amount of computer work and written comment.  You may need to seek guidance from your tutor along the way.  Do not leave things until too late!!  Please follow the instructions given with each question carefully!

Note: Your assignment should be set out using the headings under Assignment Tasks and with  answers numbered as below

The Barney Foundation is a philanthropic organization, making grants of money to various groups operating in the health, education and welfare sectors. These groups submit an application for funds to carry out some project. Each application is given an ID number which can be used to identify the order in which the applications were received. Some applications are immediately rejected since they do not meet the funding guidelines. The remainder are assessed and a decision is made. In this assignment you will examine data relating to 40 applications which were submitted during 2011 and which met the guidelines.

In 2010 there were a number of comments from both applicants for funding and also from senior staff at The Barney Foundation about the time it took the organization to reach a decision about funding – whether The Barney Foundation could fund a particular project or not. In week 14 of 2011 the CEO at The Barney Foundation set in place new policies and procedures (NP&P) in an effort to speed up the decision process.

You have been requested by the CEO to examine data and provide a statistical report. In particular, you have been asked to provide assistance in deciding whether the new policies and procedures have been successful in reducing the time taken to provide a decision on an application for funding. The CEO is interested in three issues in particular and she hopes to be able to report to the Management Committee:

• that there has been a drop in the time it takes to notify organizations of the result of an application;
• that the length of time it takes to evaluate an applications is not affected by the amount of money involved;
• that the average time it takes to evaluate an application is now below 50 days.

Data in the file find your name.xls

Random Sample: The file find your name.xls contains 51 records from which you have been given a sample of 40.  Your answers to the assignment tasks below are to be based on your sample of 40 cases.

Assignment Tasks

The Data

Sort your data by the column headed ID – remember to highlight all of your sample data before sorting. In an appendix to your report provide a printout of the data in your sample, with ID numbers in ascending order.

Time to Notification

Use a line graph to obtain a plot of the number of days from submission of an application to the applicant being notified of the result (place ID on the horizontal axis). Comment on the chart. Identify the following groups of applications, using special markers on your chart, for the first data point in group B and the first data point in group C:

1. The first group of applications (group A) for which the NP&P are not yet in place.
2. The second group of applications (group B) for which the NP&P are in place but, in your opinion, do not seem to be fully effective.
3. A third and final group (group C) of applications for which the NP&P, in your opinion, seem to be fully effective.

Explain why the chart produced in the previous question is not, properly speaking, a time series chart. (The chart does, however, place the applications in the order in which they were processed and so serves it purpose for that question.) Your explanation should include reference to the types of data used for the chart.

1. We want a chart showing how the average time to notification changes over time. To do this the data for week of submission and days to notification must be processed as follows: for each week in which one or more applications was received we require a record consisting of the number of the week and the average of the days to notification for all applications received in that week. This can be done by hand since there is not a large amount of data.

This is not the preferred method since it does not work well with large amounts of data. Your lecturer will show you two approaches to processing the data: first, how it may be done by hand and then how it may be done using the functions available in Excel (the preferred method.). In addition, we will alsore-number the weeks so that week 14, the week when the NP&P were introduced, becomes week 0.

1. a.     

The processed data is to be placed in two new columns with the headings Week of Submission and Days to Notification. Week of Submission lists all the weeks, minus 14, in which at least one application was submitted. This will start from apprximately -13 and run through to approximately  31. The exact beginning and end will depend on the sample with which you are working. This list can be easily constructed by hand.

For each of these weeks, where at least one application was received, calculate the average time to notification for applications received in that week and enter appropriately in the Week of Submission column.

Provide a printout in two columns for these new variables showing all values.

1. b.    

Now use this new data to provide a scatter plot giving a true time series chart with week of submission on the horizontal axis. On your chart weeks should be re-numbered so that week 14, the week when the NP&P were introduced, is numbered as week 0as 0 Use a special marker for this data point and also for the data point representing the week when the NP&P seem, in your opinion, to be fully effective.

1. c.      Comment on the new chart, comparing it with the previous chart produced in question 2.

Types of applications

Produce a summary table showing the mean and standard deviation for days to notification, together with the number of applications, for each of the groups A, B and C and for each type of application. Comment on the results..

Time to Evaluate and Dollar Amount

The CEO asked you to examine how the time it takes to evaluate a project varies with the amount of money involved under the NP&P.

1. Consider the data for applications made after the NP&P were in place – group C. Obtain a scatter-plot of Days to Evaluate vs Amount and fit a straight line to the data. Think carefully about which variable should be placed on the vertical axis – remember, the independent variable goes on the horizontal axis – i.e. the x-axis. (We are interested in the way in which the amount of money requested may affect the time it takes to evaluate the project.) Briefly describe the relationship.

Carry out a regression analysis on these two variables and copy the output into your assignment.

Briefly explain why you think this regression model is, or is not, a good model.

Is the time taken to evaluate an application much affected by the amount of money involved?  Can applications for small amounts of money expect a quick answer?

Evaluation Time

1. The CEO is particularly interested in the average time it takes to evaluate an application for funding. She wishes to know whether this is below 50 days for applications in group C.

Find the mean and SE for evaluation time of applications in group C. Use this to find a 95% confidence interval for evaluation times using the NP&P.

Clearly state appropriate null and alternative hypotheses for a hypothesis test of whether the population mean is below 50 days with the NP&P in place.

1. Find the test statistic and the p-value.

What do you conclude from the test?

Conclusion

Using information from your analyses write a short concluding paragraph in which you address these questions:

1. Have the NP&P been successful in reducing time to notify an applicant of the result of their application?
2. With the NP&P in place, does it seem to take longer to evaluate applications involving large amounts of money?
3. Is the average time it takes to evaluate an application less than 50 days with the NP&P in place?

SOLUTION

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