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1. A new design for the braking system for a car has been proposed. For the...

1. A new design for the braking system for a car has been proposed. For the current braking system, the true average braking distance at 40 mph under specified condition is known to be 120 ft.

It is proposed that the new braking system design will not be implemented if evidence from sample data indicates that the braking distance is HIGHER (compared to the current system).

(a) Let µ denote the true average braking distance. State an appropriate hypothesis test that would be useful in determining whether to implement the new braking system. (10 points)

(b) Test your hypothesis in question (a) using critical value approach.

Consider that Type I error α = 0.05, sample size n= 15, and X ¯= 122.5, and sample standard deviation s= 10. (20 points)

(c) Test your hypothesis in question (a) using p-value approach, with same information in question (b). (20 points)

2. A study to assess the capability of subsurface flow wetland systems to remove biochemical oxygen demand (BOD) and various other chemical constituents resulted in the accompanying data.

Here, x=BOD mass loading (kg/ha/d) and y=BOD mass removal (kg/ha/d)

x 24 26 29 32 36 40
y 32 40 39 46 50 60

(a) obtain the estimated β ^ 0 and β ^ 1coefficients, and write the linear regression equation. Show your work in excel file. (20 points)

(b) calculate SSE, SST and the coefficient of determination R 2. (20 points)

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