Section 1: Data Analysis

Using the same data set that you have been working with in the first part of the paper, please carry out the following steps:

1.1 Regress “maintenance cost” on the “engine type” dummy variable by which you divided the data set in the previous assignment.

While there is no strict requirement for the length of this assignment, I expect this first part of the paper to be about 600 to 1,000 words long.

Actual Assignment

Required steps for this first part of the paper are:

Section 1: Data Analysis

Before you start any data analysis, here’s a reminder about how to access the “Data Analysis” feature in Excel 2007 (please let me know if you are using an older version or a Mac and need assistance). Click on the “Data” tab, then select “Data Analysis” on the far right. (If “Data Analysis” is not shown there, please refer to the “Instructions on Adding in Data Analysis ToolPak” under the “Course Material” link on our Blackboard pages.)

1.1 Obtain Descriptive Statistics with Excel for the “Maintenance Cost” Variable The Bus Maintenance.xls file (posted on Blackboard with the assignment) includes data on maintenance cost of school buses and related variables.

To obtain descriptive statistics for the “maintenance cost” variable, click on “Data”, then “Data Analysis”, then “Descriptive Statistics”, then “OK”. In the dialog box, there are different ways how the “Input Range” can be entered. The easiest in my opinion is to click on the cell that contains the first value of the “maintenance cost” variable and then, while holding down the left mouse button, drag down the mouse until all values of the variable are selected. Releasing the left mouse button will paste all those values into the “Input Range” field. Then put a checkmark next to “Summary Statistics” and click “OK”. You will obtain the descriptive statistics, most of which you have encountered in your first statistics course (ECON 2100 – Business Statistics I).

1.2 Carry out a Hypothesis Test with Excel that Tests the Null Hypothesis H0: σ21 = σ22

We came across this hypothesis test in Chapter 12. Now we can use Excel to carry out the test on an actual data set with the “maintenance cost” variable. The two groups whose variances you are testing for equality are buses with Diesel engines and buses with gasoline engines.

To sort your data set by engine type, click on any of the cells in the “engine type” column and then click on the “Data” tab. You will see “AZ” with an arrow (to sort in ascending order) and “ZA” with an arrow (to sort in descending order). You can click on either of these since we only want the data to be separated into the two groups shown above.

With the data sorted appropriately, click on “Data”, then “Data Analysis”, and select “F-Test Two-Sample for Variances”, then click “OK”. In the window that opens, you need to enter the range of values of your “maintenance cost” variable for your one group (Diesel or gasoline) for the “Variable 1 Range”. Then move the cursor to the window for “Variable 2 Range” and do the same thing for the other (gasoline or Diesel) group. Click “OK”.

1.3 Carry out a Hypothesis Test with Excel that Tests the Null Hypothesis H0: μ1 = μ2

This is Chapter 11 territory. Use the same two groups (Diesel and gasoline engines) you used in the previous step.

Click on “Data”, then “Data Analysis”. In the window that opens, you need to scroll down to the appropriate test. You need to carry out either a “t=test: Two-Sample Assuming Unequal Variances” or a “t=test: Two-Sample Assuming Equal Variances”. Important: Which of these two tests is the appropriate one depends on your results from the previous section in which you tested for the equality of the variances between the two groups. The mechanics of entering data and carrying out this test are the same as in the previous hypothesis test, but please let me know if you get stuck.

Section 2: Reporting Your Results

For each data analysis that you carried out above, you must first copy and paste the results into your paper (the same way you included the ANOVA table in your Assignment 3). You then need to explain what the results mean. This part is crucial. While I feel that is very important that you know how to carry out these techniques in Excel, it is at least as important that you know what the numbers mean and how to explain them at a fairly simple level. Please write your narrative so that it is at a level that can be understood by a high school graduate who may or may not have taken some college-level coursework, but has not taken a college-level course in statistics.

More specifically, for the descriptive statistics part above, you must include the following values for the “maintenance cost” variable: Minimum value, maximum value, mean, and median. You must include a comparison of the mean to the median with a comment about how close or not close the two measures are. If the mean and the median deviate substantially from one another, you need to include an explanation for that. You must also report the standard deviation along with a brief explanation of what the standard deviation measures. (If you remember from the first statistics course—or are willing to look it up—how to use Chebyshev’s theorem or the empirical rule to give some indication on how dispersed the values are using the standard deviation, that would be a nice touch. I will not grade you on that aspect, though.)

For the hypothesis test for equal variances and for the hypothesis test for the equality of two means, you need to clearly state what the outcome of the hypothesis test is (“reject H0“ or “do not reject H0“) and what that means in non-statistical terms. Comment on whether the outcome of the tests is what you expected or what could have led to a seemingly counterintuitive outcome should you experience that.

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