Chapter 3 Applied Problems
2. Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in it mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is
MC = 40P
Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution reduction the marginal increase in revenue (MR) is
MR = 1,000 – 10P
How much pollution reduction should Appalachian Coal Mining undertake?

If Appalachian Coal Mining decided to install additional capital equipment, they would decrease the amount of pollution that their company produces. This installation of additional capital
Explain, using the appropriate p-value

Yes, Vanguard’s advertising expenditure has a statistically significant effect on the sales of Bright Side detergent. The p-value for Vanguard’s advertising equals 0.0128. This is less than 0.10, which means that their advertising is statistically significant. The p-value is “used to tell us the exact level of significance for a test statistic, which is the probability of finding significance when none exists” (Thomas & Maurice, 2011, p. 134).

d.Does advertising by its three largest rivals affect sales of Bright Side detergent in a statistically significant way? Explain, using the appropriate p-value.

Yes, the advertising by Vanguard’s three largest rivals affects the sales of Bright Side detergent in a statistically significant way. The advertising efforts of Vanguard’s rivals have a p-value of 0.0927. This is less than 0.10, making the advertising of the competitors statistically significant.

e.What fraction of the total variation in sales of Bright Side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation?
1-r2 (r-squared) = 1 – 0.2247
= 0.7753
According to the previous