Two new different models of compact SUVs have just arrived at the market. You ar

Question

Two new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of both models to see if they are the same. A partial computer output for twelve compacts SUVs of model 1 and thirteen of model 2 is given below.

Using the above information and test, the null hypothesis should be rejected.

Level of significance 0.05 Population Sample 1 Sample Size 12 Sum of Ranks 192.5 Population Sample 2 Sample Size 13 Sum of Ranks 132.5 Intermediate Calculations Total Sample Size n 25

Explanation / Answer

Assume sample standard deviation s1 =s2 = 20
mean(x)=192.5
standard deviation , s.d1=20
number(n1)=12
y(mean)=132.5
standard deviation, s.d2 =20
number(n2)=13
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.201
since our test is two-tailed
reject Ho, if to < -2.201 OR if to > 2.201
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =192.5-132.5/sqrt((400/12)+(400/13))
to =7.494
| to | =7.494
critical value
the value of |t | with min (n1-1, n2-1) i.e 11 d.f is 2.201
we got |to| = 7.494 & | t | = 2.201
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 7.494 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 7.494
critical value: -2.201 , 2.201
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that comparing the gas mileage performance of both models

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