Akiko Hamaguchi is a manager at a small sushi restaurant in Phoenix, Arizona. Akiko is concerned that the weak economic
Posted: Mon Jul 11, 2022 11:29 am
Akiko Hamaguchi is a manager at a small sushi restaurant inPhoenix, Arizona. Akiko is concerned that the weak economicenvironment has hampered foot traffic in her area, thus causing adramatic decline in sales. In order to offset the decline in sales,she has pursued a strong advertising campaign. She believesadvertising expenditures have a positive influence on sales. Tosupport her claim, Akiko estimates the following linear regressionmodel: Sales= β0 + β1Unemployment+ β2Advertising + ε.A portion of the regression results is shown in the accompanyingtable.
a-1. Choose the appropriate hypotheses totest whether the explanatory variables jointly influence sales.
multiple choice 1
H0: β1 = β2 =0; HA: At leastone βj < 0
H0: β1 = β2 =0; HA: At leastone βj ≠ 0
H0: β1 = β2 =0; HA: At leastone βj > 0
a-2. Find the value of the appropriatetest statistic. (Round your answer to 3 decimalplaces.)
a-3. At the 5% significance level, do theexplanatory variables jointly influence sales?
multiple choice 2
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 whetherthe unemployment rate is negatively related with sales.
multiple choice 3
H0: β1 ≥0; HA: β1 <0
H0: β1 =0; HA: β1 ≠0
H0: β1 ≤0; HA: β1 >0
b-2. Find the p-value.
multiple choice 4
0.01 p-value< 0.025
p-value < 0.01
p-value 0.10
0.05 p-value< 0.10
0.025 p-value< 0.05
b-3. At the 1% significance level, what isthe conclusion to the test?
multiple choice 5
Do not reject H0; we can conclude thatUnemployment is negatively related to Sales.
Do not reject H0; we cannot concludethat Unemployment is negatively related to Sales.
Do not reject H0; we can conclude thatUnemployment is positively related to Sales.
Do not reject H0; we cannot concludethat Unemployment is positively related to Sales.
c-1. Choose the appropriate hypotheses totest whether advertising expenditures are positively related withsales.
multiple choice 6
H0: β2 ≥0; HA: β2 <0
H0: β2 ≤0; HA: β2 >0
H0: β2 =0; HA: β2 ≠0
c-2. Find the p-value.
multiple choice 7
p-value < 0.01
p-value 0.10
0.05 p-value< 0.10
0.025 p-value< 0.05
0.01 p-value< 0.025
c-3. At the 1% significance level, what isthe conclusion to the test?
multiple choice 8
Reject H0 wecan conclude that Advertising is positively related to Sales.
Do not reject H0 wecan conclude that Advertising is positively related to Sales.
Do not reject H0 wecannot conclude that Advertising is positively related toSales.
Reject H0 wecannot conclude that Advertising is positively related toSales.
a-1. Choose the appropriate hypotheses totest whether the explanatory variables jointly influence sales.
multiple choice 1
H0: β1 = β2 =0; HA: At leastone βj < 0
H0: β1 = β2 =0; HA: At leastone βj ≠ 0
H0: β1 = β2 =0; HA: At leastone βj > 0
a-2. Find the value of the appropriatetest statistic. (Round your answer to 3 decimalplaces.)
a-3. At the 5% significance level, do theexplanatory variables jointly influence sales?
multiple choice 2
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 whetherthe unemployment rate is negatively related with sales.
multiple choice 3
H0: β1 ≥0; HA: β1 <0
H0: β1 =0; HA: β1 ≠0
H0: β1 ≤0; HA: β1 >0
b-2. Find the p-value.
multiple choice 4
0.01 p-value< 0.025
p-value < 0.01
p-value 0.10
0.05 p-value< 0.10
0.025 p-value< 0.05
b-3. At the 1% significance level, what isthe conclusion to the test?
multiple choice 5
Do not reject H0; we can conclude thatUnemployment is negatively related to Sales.
Do not reject H0; we cannot concludethat Unemployment is negatively related to Sales.
Do not reject H0; we can conclude thatUnemployment is positively related to Sales.
Do not reject H0; we cannot concludethat Unemployment is positively related to Sales.
c-1. Choose the appropriate hypotheses totest whether advertising expenditures are positively related withsales.
multiple choice 6
H0: β2 ≥0; HA: β2 <0
H0: β2 ≤0; HA: β2 >0
H0: β2 =0; HA: β2 ≠0
c-2. Find the p-value.
multiple choice 7
p-value < 0.01
p-value 0.10
0.05 p-value< 0.10
0.025 p-value< 0.05
0.01 p-value< 0.025
c-3. At the 1% significance level, what isthe conclusion to the test?
multiple choice 8
Reject H0 wecan conclude that Advertising is positively related to Sales.
Do not reject H0 wecan conclude that Advertising is positively related to Sales.
Do not reject H0 wecannot conclude that Advertising is positively related toSales.
Reject H0 wecannot conclude that Advertising is positively related toSales.