Specific Motors of Detroit has developed a new Automobile kn

Specific Motors of Detroit has developed a new Automobile known as the M Car. 24 M cars and 28 J cars (from Japan) were road tested to compare miles-per-gallon (mpg) performance. The sample statistics are shown below: Sample 1(M-Cars) Sample 2 (J Cars)

Sample 1(M-Cars)

Sample 2 (J Cars)

n1 = 24

n2= 28

S1 = 2.56 S2 = 1.81

Calculate a 90% confidence interval for the difference between mpg performance of the 2 car models.

A.) The manager claims that there is no difference in the mpg performance of M and J cars.

B.) Write out the null and alternative hypothesis to test the manager’s claim. [2]

C.) Calculate the test statistic. [2]

D.) Calculate the p-value. [3]

E.) At a 5% level of significance do you accept or reject Ho. [1]. Explain why [1].

Solution

A)
Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
C)
Test Statistic
X(Mean)=29.8
Standard Deviation(s.d1)=2.56 ; Number(n1)=24
Y(Mean)=27.3
Standard Deviation(s.d2)=1.81; Number(n2)=28
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =29.8-27.3/Sqrt((6.5536/24)+(3.2761/28))
to =4
| to | =4
D)
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 4.0028 ) = 0.001
Hence Value of P0.05 > 0.001,Here we Reject Ho
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 23 d.f is 2.069
We got |to| = 4.00284 & | t | = 2.069
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho