Question

5. The profits (in millions) of 200 firms 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 = 11.25 + 7.40Tech - 3.88Manuf -0.80Age - 0.95TaxRate (4.80) (4.62) (3.15) (0.35) (1.20) a) Test the hypothesis that the age of the firm has no effect on profits against the alternative that it does have an effect at the 95 percent confidence level? b) Test the hypothesis that being a manufacturing firm has no effect on profits against the alternative that it does have an effect at the 90 percent confidence level? c) Test the hypothesis that the tax rate has no effect on profits against the alternative that is has a negative effect at the 95 percent confidence level. d) What is the 99% confidence interval for the effect of age on profits?

Answer 1

For the hypothesis testing we will use the t-test.

If the calculated t statistic > Tabulated t statistic, then we will reject the null hypothesis.

The estimated model is  

Profits = a + B.Tech - B Manuf - B3 Age - B Tax Rate

Where,

a = 11.25,31 = 7.40, B2 = -3.88, B3 = -0.80, B4 = -0.95

The t test is estimated using ..................................... (1)

Bi t = SEB)

Here, i= 1,2,3,4.

Null Hypothesis (H₀):

Bi(population) = 0

Alternative Hypothesis (H₁):

Bi(population) = 0

For all the following questions we will be following the (1) formula.

The degrees of freedom for the model is n-k-1 = 200-4-1 = 195

Answer to question a:

B3 -0.80 SE = 0.35 = -2.29

At 5% level of significance with 195 degrees of freedom the tabulated value of |t| statistic is |1.96| which is less than the calculated t statistic |2.29|. So, we can reject the null hypothesis and can conclude that Age of the firm has a significant effect on the profit.

Answer to question b:

B2 -3.88 _123 133 = SEB) = 3.15 = -1.23

At 10% level of significance with 195 degrees of freedom the tabulated value of |t| statistic is |1.64| which is greater than the calculated t statistic |1.23|. So, we can not reject the null hypothesis and can conclude that the manufacturing firm has no significant effect on the profit.

Answer to question c:

4 -0.95 tiga = SE(BA) = 1.20 = -

At 5% level of significance with 195 degrees of freedom the tabulated value of |t| statistic is |1.96| which is greater than the calculated t statistic |0.79|. So, we can not reject the null hypothesis and can conclude that the tax rate has no significant negative impact on the profit.

Answer to question d:

B3 -0.80 SE = 0.35 = -2.29

At 1% level of significance with 195 degrees of freedom the tabulated value of |t| statistic is |2.576| which is greater than the calculated t statistic |2.29|. So, we can not reject the null hypothesis and can conclude that Age of the firm has a no significant impact on the profit.

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