Suppose mu1 and mu2 are true mean stopping distances at 50 m

Suppose mu_1 and mu_2 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 0.01 to test H_0: mu_1 - mu_2 = -10 versus H_a: mu_1 - mu_2

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 > u2
Alternate Hypothesis, There Is Significance between them - H1: u1 < u2
Test Statistic
X(Mean)=115.6
Standard Deviation(s.d1)=5.07 ; Number(n1)=5
Y(Mean)=129.1
Standard Deviation(s.d2)=5.31; Number(n2)=5
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =115.6-129.1/Sqrt((25.7049/5)+(28.1961/5))
to =-1.065
| to | =1.065
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 4 d.f is 2.132
We got |to| = 1.065 & | t | = 2.132
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Left Tail - Ha : ( P < -1.065 ) = 0.17345
Hence Value of P0.05 < 0.17345,Here We Do not Reject Ho