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ID: 3375604 • Letter: M
Question
MUST SHOW ALL WORK PLEASE AND THANK MUST SHOW ALL WORK PLEASE AND THANK MUST SHOW ALL WORK PLEASE AND THANK
Does the weight of a vehicle affect the gas mileage? The following random sample was collected where x= weight of vehicle in hundreds of pounds and y= miles per gallon.
1) The linear correlation is determined to be r= -.9701. Conduct an appropriate hypothesis test to determine if the weight and MPG of the vehicle are correlated.
2) The regression equation is determined to be MPG 32.5 - 0.45x weight. What is the predict MPG for a car weighting 24 hundred pounds?
3) what is the predictied weight for a car that gets 22 MPG?
4) Find and interpret the y intercept of the regression equation. Is this a useful value in this context?
5) Find and interpret the slope of regression equation.
(20 points) Does the weight of a vehicle affect the gas mileage? The follow sample was collected where x - weight of a vehicle in hundreds of pounds ana per gallon. ing r eds of pounds and y mi x (lb hundreds) 26 35 29 39 20 y (mpg) 22.0 16. 18.8 15.7 23.4Explanation / Answer
A)
Ho: the value of correlation Coefficient is not significant. H1: the value of correlation Coefficient is significant.
R=-0.9701
n= 5.0000
t = r*sqrt((n-2)/(1-r^2))
-0.9701*SQRT((5-2)/(1--0.9701^2))
-6.923
P-value
2*(1-P(T<|t|)
2*(1-P(T<abs(-6.92304894906846))
T.DIST.2T(abs(-6.92304894906846),5-2)
0.0062
With (t=-6.923, p<5%), the null hypothesis is rejected at 5% level of significance. And I can conclude that the value of correlation Coefficient is significant. In other words I can say that weight and mpg of a vehicle are correlated.
B)
MPG = 32.5-0.45*weight
=32.5-0.45*24
=21.7
C)
MPG = 32.5-0.45*weight
=32.5-0.45*22
=22.6
D)
Intercept = 32.5
The initial value of mpg is 13.5 when the weight is 0 pounds.
E)
The slope is equal to-0.45
With one 100 of Pound increase in weight of the vehicle, there are 0.45 miles per gallon decrease in the value of mpg