Question

In: Statistics and Probability

Dep.= Mileage Indep.= Octane SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard...

Dep.= Mileage Indep.= Octane
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations 7.0000
ANOVA
Significance
df SS MS F F
Regression 9.1970
Residual
Total 169.4286
Standard
Coefficients Error t Stat P-value Lower 95% Upper 95%
Intercept -115.6768
Octane 1.5305
SE CI CI PI PI
Predicted Predicted Lower Upper Lower Upper
x0 Value Value 95% 95% 95% 95%
89.0000 1.4274
87.0000 2.0544

Is there a relationship between a car's gas MILEAGE (in miles/gallon) and the OCTANE rating of its gas? Use the excel output above to answer the following question.

What is the 95% confidence interval for the mean gas mileage of cars that use 89 octane gas (without units)?

a.

(17.6615, 23.4139)
b.

None of the answers is correct
c.

(18.4309, 22.6445)
d.

(16.8679, 24.2075)
e.

(17.0449, 24.0305)

Solutions

Expert Solution

X Value=   89      
Confidence Level=   95%      
          
          
Sample Size , n=   7      
Degrees of Freedom,df=n-2 =   5      
critical t Value=tα/2 =   2.571   [excel function: =t.inv.2t(α/2,df) ]  

Predicted Y at X=   89   is          
Ŷ =   -115.6768   +   1.5305   *89=   20.538

standard error, S(ŷ)= 1.427              
margin of error,E=t*Std error=t* S(ŷ) =   2.5706   *   1.427   =   3.6692
                  
Confidence Lower Limit=Ŷ +E =    20.538   -   3.669   =   16.8685
Confidence Upper Limit=Ŷ +E =   20.538   +   3.669   =   24.2069

answer:  

(16.8679, 24.2075)

orchestra answered 3 years ago
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