Q3 a Suppose mu1 and mu2 are true mean stopping distances at

Q3 (a) Suppose mu1 and mu2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance Level .01 to test H0 : mu1 - mu2 = -10 versus Ha : mu1 - mu2

Solution

(a)

H0 : mu1 -mu2 = -10

Ha : mu1 -mu2 < -10

Standard Error SE = sqrt[ (s₁²/n₁) + (s₂²/n₂) ]

= sqrt( (5.03)^2/6 + (5.38)²/6 )

=3.007

t = [ (x₁ - x₂) - d ] / SE

t = (( 115.7 - 129.3) - ( -10 ))/ 3.007 = -1.2

DF = ( 6 -1 )+(6-1) = 10

Critical t* value = 2.764

Since : t* > t

Failed to reject null hypothesis

(b)

P-value approach:

t = -1.2

P-value = 0.1151

Since P-value > 0.01

Failed to reject null hypothesis.