## Question

###### Akiko Hamaguchi is a manager at a small sushi restaurant in Phoenix, Arizona, Akiko is concerned...

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 the following linear regression model: Sales = Bo + B1 Unemployment + B2Advertising + E. A portion of the regression results is shown in the accompanying table. Use Table 2 and Table 4 ANOVA Regression Residual Total df 2 14 16 SSM S 74.0574 37.0287 59.4638 4.2474 133.521 Significance F 0.0035 Intercept Advertising Unemployment Coefficients 18.9260 0.0277 -0.6868 Standard Error 3.9859 0.0080 0.3039 Stat p-value 4.7482 0.0003 3.4625 0.0038 -2.26000.0403 Lower 95% 10.38 0.01 -1.34 Upper 95% 27.47 0.04 -0.03 a-1. Choose the appropriate hypotheses to test whether the explanatory variables jointly influence sales. Ho: B4 = B2 = 0; HA: At least one B;> 0 O Ho: B1 = B2 = 0; HA: At least one B, 0 Ho: B4 = B2 = 0; HA: At least one B, O 3-2. Find the value of the appropriate test statistic. (Round your answer to 3 decimal places.) Test statistic 1.235 3-3. At the 5% significance level, do the explanatory variables jointly influence sales? Yes, since the F test is significant Yes, since all t-tests are significant.

Both answers are correct. b-1. Choose the hypotheses to test whether the unemployment rate is negatively related with sales. O Ho: B230; HA: B2>0 Ho: B220; HA B2 <0 Ho: B2 = 0; HA B2 #0 b-2. Find the p-value. (Round your answer to 4 decimal places.) p-value b-3. At the 1% significance level, what is the conclusion to the test? Reject HO; the unemployment rate and sales are negatively related Do not reject HO; we cannot conclude the unemployment rate and sales are negatively related. Do not reject HO: We can conclude the unemployment rate and sales are positively related. Do not reject HO: we cannot conclude the unemployment rate and sales are positively related. 0-1. Choose the appropriate hypotheses to test whether advertising expenditures are positively related to sales. Ho: B1 = 0; HAB, *0 Ho: B420: HAB, <0 Ho: B, SO: HAB, >O 6-2. Find the p-value. (Round your answer to 4 decimal places.) p-value 3. At the 1% significance level, what is the conclusion to the test? Reject Ho: advertising expenditures and sales are positively related Do notret HO, we cannot conclude advertising expenditures and sales are positively related Do not reject Ho: we can conclude advertising expenditures and sales are positively related Reject advertising expenditures and sales are not positively related Hints References Book & Resources

## Answers

a-2)test statistic =MS(regression)/MS(error )=37.0287/4.2474=8.718

b-1)

b-2)

p value =0.0201

b-3)

do not reject, we can not conclude,,,,,,,,,,,,

c-1)

c-2)

p value =0.0019

c-3) reject Ho we can conclude,,,,,,,

Ho: B220; HA B2 <0Ho: B, SO HAB, > 0

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