The profits of 200 firms (in millions) are estimated as a function of whether th
ID: 3236447 • Letter: T
Question
The profits of 200 firms (in millions) are estimated as a function of whether the firm is in the tech, retail, or manufacturing sector, the age of the firm in years, and the tax rate (in percentage points). Standard errors are shown in parentheses. Profits = 13.7 + 18.5Tech - 9.4Retail - 1.4Age - 1.1TaxRate a) Does the age of the firm have a statistically significant effect on profits at the 90 percent confidence level? At the 95 percent confidence level? b) Test the hypothesis that the tax rate has a negative effect on profits at the 90% confidence level. c) What is the 95% confidence interval for the effect of being a tech company on profits?Explanation / Answer
a. We need to check value of age coefficient is significantly different from 0 or not
t = -1.4/0.8 = -1.75
Degrees of freedom = 200-5 = 195
At 90% CI, 2 tailed test:
t_crit = t0.95,195 = 1.653. So, |t| > t_crit. Hence null hypothesis is rejected and slope coefficient of age is significant
At 95% CI, 2 tailed test:
t_crit = t0.975,195 = 1.972. So, |t| < t_crit. Hence null hypothesis is not rejected and slope coefficient of age is not significantly different from 0
b. H0: Slope coeff = 0
H1 : Slope coeff not equal to 0
t value for coefficient of tax rate = -1.1/1.8 = -0.611
t_crit = t0.95,195(2 tailed at 90% Confidence = 1.653. Hence null hypothesis is not rejected and coefficient is not significantly different from 0
c. At 95% CI, t value = t0.975,195 = 1.972
Hence 95% CI is (18.5-1.972*4.6, 18.5+1.972*4.6) = (9.4288, 27.5712)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.