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Managerial Economics (T-Statistic; F-Test; Null Hypothesis)

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Famous Electronics sells TV satellite dishes and has been in business for a number of years. The firm's owner has become concerned about the firm's pricing, advertising, and other competitive strategies. She hired a consulting firm to estimate the demand function for TV dishes. The consulting firm informed her that the demand function was estimated using data gathered from 150 similar firms operating during the past year. Standard deviations of each of the regression coefficients are reported in parenthesis.

Qx = 1500 - 0.8 Px + 20 Pc + 0.032 Y + 0.012 Ax
(240) (0.17) (4.5) (0.007) (0.002)

R2 = 0.25
Standard Error of the estimate = 40.0

where: Qx = annual quantity of dishes sold
Px = the price per dish
Pc = the price of regular cable TV service
Y = average income
Ax = advertising expenditures on dishes

Current values for the independent variables are: Px = 1,500; Pc = 60; Y = 45,000; and Ax = 50,000

Use t-statistic or F-test and null hypothesis wherever applicable:

a. Calculate the expected quantity of dishes to be sold, given the current values of the independent variables.
b. Construct and interpret the meaning of a 95% confidence interval around the estimated quantity of dishes to be sold as forecasted in part a.
c. What proportion of total inter-firm variation in quantity sold is explained by the model? Is this value significantly different from zero, assuming a desired 95% confidence level?
d. Calculate and interpret the economic meaning of the point demand elasticity corresponding to each of the model's independent variables Px, Pc, etc.

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