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# Answer the math problem - Speech or Presentation Example

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Stata is available in Eller’s computer lab. A 6-month student license for Stata can also be purchased for \$35. R is a free language downloadable here:…

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Prof. Kathie Barnes Economics 439 Law, Economics & Statistics DUE: Tuesday, March24, at the beginning Directions: Thishomework is your chance to get started using Stata or another statistical program of your choice. Stata is available in Eller’s computer lab. A 6-month student license for Stata can also be purchased for \$35. R is a free language downloadable here: http://www.r-project.org. (I suggest R only for those students who have some programming experience). SAS, SPSS, and Matlab are all available in all UA OSCR labs as well. You must turn in a log of your work in the program of your choice. Do not use Excel – take this opportunity to learn the statistical program that you’ll need for the final project.
1. Parking Meter Heist, revisited
(A) Perform a t-test testing whether CDC and Brinks have the same average collections per day for the area that they were responsible for (ie, not 1-A). Show your work, either via calculations or providing a log of your stata session (or other program) or the formulas you used in excel. Can you use the result to create an estimate of the total amount stolen from June 1979-April 1980 (10 months)? If you can, do so. If not, explain why.
To use STATA or any other software, create a data set with average collections for CDC and average collections for Brinks as the only two variables.
Using the command ttest brinks==cdc, where brinks is the average collection for brinks and cdc is the average collection for CDC. The STATA results are as follows:
From the results, note that the p-value is 0.0001, for the absolute difference in the means. This implies that the mean of average collections between the two companies is statistically different at a significant level of 5%.
The t test shows the statistical difference between either two variables or a variable and a constant but cannot be used for estimation. Therefore determining, the total amount stolen requires an estimation method, different from t-test such as regression.
(B) Create a 95% confidence interval for the average amount stolen per month based solely on the difference between CDC and Brinks time periods (ie, use the same data as (A). Again, show your work, either via calculations or providing a log of your STATA session (or other program) or the formulas you used in excel.
(C) Create a 95% confidence interval for the total amount stolen over the 10 month period June 1979-April 1980 using your estimate from part (B)
Total amount stolen = mean * 10
For Brinks
Lower limit = 73437.33 *10 = 734,373.3
Upper limit = 79963.5 *10 = 799,635
Therefore:
734,373.3 ≤ total amount stolen at brinks ≤ 799,635
At CDC,
Lower limit = 84318.2*10 = 843,182
Upper limit = 92138.17 *10 = 921381.7
Therefore:
843,182 ≤ total amount stolen at brinks ≤ 921381.7
(D) Create a new variable called “winter” that is equal to 1 from November – February, and 0 otherwise. Create a second new variable called “summer” that is equal to 1 from June-August. Summarize these variables; what are their means and standard deviations?
(E) Using the entire data (CDC, Brinks, and Wells Fargo time periods), test whether summer is different from winter. Explain your results.
Note that the p-value is 0.4556, implying that there is a difference between winter and summer.
2. Regression example, cell phone carriers. (Data available on Blackboard).
You are trying to decide whether to use T-Mobile, AT&T or Verizon as your cell phone carrier. You have data on average costs each month over a series of years for an individual who has similar phone habits (for data, texting and voice). The only difference is that this person travels internationally in the summer, and so has a higher bill then.
(A) Load the data into your statistical program and create a variable that takes the values 1,2,3 for the three different cell phone carriers. Create a dummy variable for summer (ie, it equals 1 if the bill was during the summer and 0 otherwise. (Hint: you can use two lines with the generate command and then the replace command)
(B) Perform a t-test comparing T-Mobile cost to AT&T cost. Explain your results.
Using the variable price1 to represent average cost for T-mobile and price2 to represent average cost for AT&T. the t-test results are as follows
Therefore, with the probability of t (0.0352), smaller than the significant level, it can be concluded with 95% confidence that at the average costs of the two companies are not statistically different. However, price2 is not less than price1, (see that pr(T>t) =0.9824)
(C) Perform a regression with dependent variable of Cost and independent variable of i.carrier (ie, dummy variables for each carrier). Explain your results. Can you compare T-Mobile cost to AT&T cost using the results? If so, do so.
From the table, the estimated model is thus
Cost = 128.49 -4.498 c1 + 16.038c2 +
Where cost is the expected average cost
C1 = 1 if the carrier is t-mobile and 0 otherwise
C2 = 1 if the carrier is A&T and 0 otherwise
Summer = 1 if the cost was undertaken in winter and 0 otherwise
An average an individual is expected to spent 128.49 if he chooses Verizon. By choosing T-mobile the expenditure reduces by 4.498, while use of AT&T increases the cost by 16.038, notably the choice of a mobile carrier influences cost, by the coefficient. Therefore, to compare the costs between AT&T and T-mobile, get the difference between the coefficients.
16.038- (-4.498)
= 20.536’
Therefore, choosing T-mobile is cheaper by 20.536 as compared to using AT&T
(D) Add another variable, summer, to the regression. How does this change the results? Which carrier is cheapest? How can you tell?
Cost = 121.0718 -0.5386c1 + 11.9134c2 + 34.648summer
Where:
Summer = 1 if the cost was undertaken in winter and 0 otherwise
T-mobile is the cheapest carrier. Though the coefficient of c1 is not statistically significant, it has a negative sign implying that –mobile expenditure is less than the indicator variable Verizon. Read More
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