Question

Suppose µX and µY are the true mean stopping distances when starting at 50 mph for cars of a
certain type equipped with two different braking systems (System X vs. System Y). The
following data was obtained for each braking system:

System X    System Y
nx = 8           ny = 8
x = 85.7 ft    y = 96.3 ft
sx = 4.36 ft sy = 5.18 ft
Consider the following hypotheses:
Ho: µX - µY = -5
Ha: µX - µY < -5
As indicated by the alternative hypothesis, it is believed that cars equipped with System X
are able to stop over a shorter distance than cars equipped with System Y. Does the data
support this hypothesis at the 1% level?

Answer 1

Ho: µX - µY = -5
Ha: µX - µY < -5

Firstly to conduct this we need to check the assumption of homogeneity of variances

So for that

F= sx^2/sy^2

F= (4.36)^2/(5.18)^2

F= 0.708

P value= 0.6699> 0.05 level of significance therefore not significant . Hence variances are equal.

Now

We can proceed with indepednent t test

where sp is pooled stanadrd deviation

Pooled Standard Deviation: 4.7876

d.f =8+8-2= 14

The P-Value is .017308. The result is not significant because p > .01.

Decsion: Fail to reject null hypothesis H0.

Conclusion: We don't have sufficient evidence to conclude that  cars equipped with System X
are able to stop over a shorter distance than cars equipped with System Y at 0.01 level of significance.