Question

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)

Answer 1

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)