Question

#9 need help all of it

SUMMARY OUTPUT Regression Statistics Multiple R 0.89079322 R Square Adjusted R S 0.78995244 Standard Erro 3.04000462 Observations 0.79351257 60 ANOVA MS Significance F df Regression 1 2059.8551 2059.8551222.888768 1.5799E-21 58 536.014429 9.24162808 59 2595.86953 3 Residual Total er 95% Lower 98.0% Upper 98.0% 4.70337792 0.85182782 5.52151244 8.2562E-07 2.99825928 6.40849657 2.66548423 6.74127162 ertising 2.04813433 0.13718744 14.9294597 1.5799E-21 1.77352384 2.32274483 1.7199302 2.37633847 Coefficients Standard Errot Stat P-value Lower 95% Intercept Adv 9. A marketing manager claims that an expenditure of $1000 results in an average profit increase of $1650. State the Hypotheses to test this claim Calculate the Test-statistic. Would you reject the Null Hypothesis at a -0.05 level? State yes or no and explain precisely the basis for your decision. Would you reject the Null Hypothesis at α =0.02 level? State yes or no and explain precisely the basis for your decision.

Answer 1

Question 9

Solution:

We are given that an expenditure of $1000 results in an average profit increase of $1650.

This means, an expenditure of $1 results in an average profit increase of $1.65.

Slope is 1.65.

The null and alternative hypotheses are given as below:

H₀: β₁= 1.65

H₁: β₁ ≠ 1.65

Test statistic for this test is given as below:

t = β̂/SE(β̂) = 2.0481/0.1372 = 14.92784257

P-value = 0.00

(by using given excel regression output)

P-value < α = 0.05

So, we reject the null hypothesis

There is insufficient evidence to conclude that the population slope is 1.65.

In simple language, there is not sufficient evidence to conclude that an expenditure of $1000 results in an average profit increase of $1650.

For α = 0.02

P-value = 0.00 < α = 0.02

So, we reject the null hypothesis

There is insufficient evidence to conclude that the population slope is 1.65.

In simple language, there is not sufficient evidence to conclude that an expenditure of $1000 results in an average profit increase of $1650.