Week 5 Problems
January 11, 2011
1. SupplyCo. is a supplier to a number of firms in an industry. By carefully mining its customer data warehouse, SupplyCo. reveals a plausible new model for manufacturing and distributing industry products that would increase the overall efficiency of the industry system, reduce costs of production (leading to greater industry profits and more sales for SupplyCo.), and result in greater sales and profits for some of the industrys manufacturers (SupplyCo.s customers).
On the other hand, implementing the model would hurt the sales and profits of other firms that are also SupplyCo.s customers but which are not in a position (due to manpower, plant, or equipment) to benefit from the new manufacturing/distribution model. These firms would lose sales, profits, and market share and potentially go out of business.
Does SupplyCo. have an obligation to protect the interests of all its customers and to take no action that would harm any of them, since SupplyCo. had the data within its warehouse only because of its relationship with its customers (It would betray some of its customers if it were to use the data in a manner that would cause these customers harm.) Or does it have a more powerful obligation to its stockholders and employees to aggressively pursue the new model that research reveals would substantially increase its sales, profits, and market share against competitors
a. What are the most prudent decisions SupplyCo. can make about its responsibilities to itself and others
If Supply Co. drives its customers out of business then this will hurt the company however if the overall sales with the new product can exceed any losses, it would be a great business decision. There is the potential for a distribution agreement with customers to sell the new product under a label (private) then there is the potential for a broad range of benefits. Supply Co has to manager the new product and business for the best return for the investors while creating a balance for the consumers.
b. What are the implications of those decisions even if there is no violation of law or regulation
You have to ensure that there is a balance not only to the investors but to the consumers and not at the cost of social consciousness. If a business is not concerned about this then you could have the potential for corporate scandals that have occurred over the past years.
2. The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asks the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.
City Police Crime Count
Oxford 15 17
Starksville 17 13
Danville 25 5
Athens 27 7
Holgate 17 7
Carey 12 21
Whistler 11 19
Woodville 22 6
a. If we want to estimate the number of crimes based on the number of police officers, which variable is the dependent variable and which is the independent variable
The crime count is the dependent variable and the police count is the independent one.
b. Draw a scatter diagram using the graphing features of Excel.
c. Determine the coefficient of correlation and coefficient of determination.
-0.87440 police and crime is negatively correlated as expected.
d. Interpret these two statistical measures. What does that tell you about the relationship between police force size and crimes
0.7646 and 76 percentage of variation in data is explained by police
Variable and basically regression equation is given by following crime = 29.338 – 0.9596 which tells us that increase in police will decrease in crimes.
3. The Airline Passenger Association studied the relationship between the number of passengers on a flight and the flight cost. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a sample of 15 flights, the correlation between the number of passengers and total fuel cost was .667.
Is it reasonable to conclude that there is positive association in the population between the two variables Use the .05 significance level.
The null hypothesis tested is
H0: ? =0 (?- population correlation coefficient)
H1: ? ? 0
Test Statistic used is
Rejection criteria: Reject the null hypothesis , if the calculated value is greater than critical value of t with (n-2) d.f at 0.05 significance level
Details
= 13.2134
Significance Level =0.05
d.f =23
Critical value = ?2.069
Since the calculated value of | t | is greater than the critical value, we reject the null hypothesis. Thus the correlation coefficient is significant at 0.05 significance level.
4. The president of a financial services group believes there is a relationship between the number of client contacts and the dollar amount of sales. He gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.
Contacts Sales
14 24
12 14
20 28
16 30
46 80
23 30
48 90
50 85
55 120
50 110
a. Determine the regression equation. Is this a significant regression at the .05 level
The regression equation would be f (# of contacts) = 2.195 (# of contacts)-12.20. There is a relationship between the number of client contacts and the dollar of amount of sales.
b. Using the regression equation, determine the estimated sales if 40 contacts are made.
The number of estimated sales if 40 contacts are made are f(40)=75.6
5. The following data show the retail price for 12 randomly selected laptop computers along with their corresponding processor speeds in gigahertz.
Machine # Speed Price
1 2 $2,689
2 1.6 1,229
3 1.6 1,419
4 1.8 2,589
5 2 2,849
6 1.2 1,349
7 2 $2,929
8 1.6 1,849
9 2 2,819
10 1.6 2,669
11 1 1,249
12 1.4 1,159
a. Develop a linear equation that can be used to describe how the price depends on the processor speed. Is this a significant regression at the .05 level
The general form of simple linear regression is Y= a + bX
b. Based on your regression equation, is there one machine that seems particularly over or underpriced State the number of the machine and the evidence that suggests it is over or underpriced.
Observation Price Predicted Price :Y Residuals
1 $2,689 2434.717 224.2827
2 1229 1918.829 -689.829
3 1419 1918.829 -499.829
4 2589 1144.996 444.0043
5 2849 2434.717 -585.717
6 1349 1402.94 -53.94
7 2929 2434.717 494.2827
8 1849 1918.829 -69.8287
9 2819 2434.717 384.2827
10 2669 1918.829 750.1713
11 1249 1144.996 104.0043
12 1159 1660.884 -501.884
The 10th computer is highly overprices as it price is much higher than the predicted value. The second machine is under priced as its price is less than the predicted value.
c. Compute the correlation coefficient and the coefficient of determination between the two variables. At the .05 significance level conduct a test of hypothesis to determine if the population correlation could be greater than zero.
Thus there is positive correlation between the variables.
The null hypothesis tested is
H0: ? =0 (?- population correlation coefficient)
H1: ? > 0
Details
= 3.1919
Significance Level =0.05
d.f =10
Critical value = 1.81
Since the calculated value of t is greater than the critical value, we reject the null hypothesis. Thus the correlation coefficient is significant at 0.05 significance level.