Akiko Hamaguchi is a manager at a small sushi restaurant in

Akiko Hamaguchi is a manager at a small sushi restaurant in Phoenix, Arizona. Akiko is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. In order to offset the decline in sales, she has pursued a strong advertising campaign. She believes advertising expenditures have a positive influence on sales. To support her claim, Akiko estimates a regression model as Sales = ₀ + ₁Advertising + ₂Unemployment + . A portion of the regression results follows.

Find the value of the appropriate test statistic. (Round your answer to 3 decimal places.)

Find the p-value. (Round your answer to 4 decimal places.)

Solution

a1.

Null Hypothesis: H₀: ₁ = ₂ = 0;

Alternative Hypothesis: H_A: At least one _j 0

a2.

The test statistic , F = 8.760

a3..

Both answers are correct.

For p-value of F-score <0.05. Also P-value for t scores<0.05.

b1.

Null hypothesis: H₀: ₂ 0;

Alternative Hypothesis : H_A: ₂ < 0

b2.

from anova table

P-value = 0.0377    

b3.

Since P-value <0.05 we fail to reject the null hypothesis

Do not reject H₀; the unemployment rate and sales are not negatively related.

c1.

Null Hypothesis: H₀: ₁ 0;

Alternative Hypothesis: H_A: ₁ > 0

c2.

P-value: = 0.0015    

c3.

Do not reject H₀; advertising expenditures and sales are not positively related.