Determine the mean, standard deviation and standard error for the last three years of quarterly data.

Paper, Order, or Assignment Requirements

 

 

STATS1900 Business Statistics

 

Major Assignment

27/2014

 

 

Date Due:         Refer to Unit Description

Total Marks:  40 marks                                         

Worth: 20% of final assessment

This assignment requires an 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!! Each question carefully describes what you are required to do so please follow these carefully!

In this assignment you will examine quarterly accident data obtained from a large company that employs up to 18000 people. Each accident costs the company time and money, and the worker usually has considerable pain and suffering. This company has introduced new work procedures in the hope that the numbers of accidents can be reduced and that their safety performance might be improved. The data is contained in the file Accident Data.xls and contains the following columns (variables):

 

Variable Description
ID Identification number from original file
Qtr Quarter
Accidents Number of accidents
Est-EFT Estimated number of Full Time Employees
#/1000 Number of accidents per 1000 Full Time Employees
WDL/Qtr Number of Working Days Lost per Quarter
WDL/1000EFT Number of Working Days Lost per 1000 Full Time Employees

 

Random Sample: Before you begin your analysis you are required to take a random sample of size 24 from the 38 cases in the file. Use the file Sample-Generator-102.xls to do this. Your tutor will show you how this can be done in EXCEL. Your answers to the assignment tasks below are to be based on your sample of 24 cases. Make sure to keep a safe copy of your sample since you cannot use Sample-Generator-102 to reproduce the first sample.

 

To prepare your data file ready for analysis you must follow the following steps:

  1. Use the Sample-Generator-102 file to generate a random sample of 24 from the file Accident Data.xls.
  2. After you have generated your sample you need to sort your data by the column headed ID – remember to highlight all of your sample data before sorting.
  3. You may have noticed that the second column headed Qtr is empty. Fill the second column with the numbers 1 to 24. These numbers represent quarters and because there are 24 of them you have 6 years of quarterly data.
  4. Copy your sample file to another spreadsheet for working your assignment. Make sure you save your random sample.
  5. Now you are ready to use your sample data to complete the assignment tasks listed below

 

 

2 marks

Provide a printout of the data in your sample, with ID numbers in ascending order.

 

Assignment Tasks

 

  1. Historically this company believed that their average number of quarterly accidents was relatively stable at 56 accidents per quarter. For the last three years the company has insisted that all workers wear protective clothing at all times, including hard hats, steel-capped boots, strong gloves, protective glasses, and so on.
3 marks
2 marks

Determine the mean, standard deviation and standard error for the last three years of quarterly data. Use this information to carry out a t-test to see if the average number of quarterly accidents for the last three years is significantly less than 56.

 

2 marks
2 marks
2 marks

Obtain a scatter-plot of the quarterly number of accidents vs working days lost per quarter. Think carefully about which variable should go on the vertical axis – remember, it is the independent variable that goes on the horizontal axis (i.e. the x-axis). Make sure you label your axes properly and your graph has an appropriate title. Briefly describe the nature of the relationship between these two variables.

 

1 marks

Using Tools>Data Analysis in XL carry out a regression analysis on these two variables. Copy the output into your assignment and use it to determine the following:

 

1 mark

Write down the regression equation

 

3 marks

State the R-Square value and the Standard Error and explain what they mean with respect to this data.

 

2 marks

Write down the value of the gradient of the regression line and explain what it means in this case.

 

2 marks

Is the constant or intercept value significant in this case? How do you know this?

 

2 marks

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

 

3 marks

Obtain a time series plot of the number of accidents per quarter. Describe the nature of this time series and identify which of the four time series components are present in this case.

2 marks

Compare the first half of the time series to the second half (i.e. the first three years with the last three years), and briefly describe any differences.

3 marks
2 marks

By right clicking on one of the data points, add a trend line to the time series, making sure you include the regression equation and the R-Square value. Interpret the meaning of the slope coefficient in this case and state whether or not this is good for the company.

2 marks
2 marks

Use the regression equation to de-trend the data placing the de-trended data in another column. Obtain a time series plot of the de-trended data and explain what it shows.

 

2 marks

Using information from your analyses write a short concluding paragraph about whether or not the company has been successful in trying to reduce the number of quarterly accidents for its workers.

 

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