Question

1.)
A mechanical. person is intrested in testing if tuning a car engine would improve the gas miliage. A simple random sample of 8 cars were selected to determine the milage (miles per gallon). Then each of the 8 cars were given a tune up

Data
After Tune up: 28.21, 29.4, 30.42, 29.67, 31.31, 29.68, 28.82, 29.38
Mean: 29.61
Standard Deviation: 0.94

Before Tune Up: 26.9, 26.37, 29.13, 28.46, 28.17, 27.67, 27.84, 27.18,
Mean: 27.72
Standard deviation: 0.89

Difference (After-Before): 1.31, 3.03, 1.29, 1.21, 3.14, 2.01, 0.98, 2.2,
Mean: 1.9
Standard Deviation: 0.84

1.) Are the 2 samples (Before and after Tune Mileage) independent or dependent? Explain

2.) Show which plot you would use to check your assumptions? Show picture of it

3.)Are their and serious violations of any other assumption plots? Explain

4.) What is your output? state below Explain why you chose this output

5.) What is your conclusion at a 5% confidence level?

Answer 1

1.

Given that,
null, H0: Ud = 0
alternate, H1: Ud > 0
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.895
since our test is right-tailed
reject Ho, if to > 1.895
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 1.896
We have d = 1.896
pooled variance = calculate value of Sd= √S^2 = sqrt [ 33.725-(15.17^2/8 ] / 7 = 0.842
to = d/ (S/√n) = 6.371
critical Value
the value of |t α| with n-1 = 7 d.f is 1.895
we got |t o| = 6.371 & |t α| =1.895
make Decision
hence Value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 6.3713 ) = 0.00019
hence value of p0.05 > 0.00019,here we reject Ho
ANSWERS
---------------
1.
the 2 samples (Before and after Tune Mileage) dependent
2.
Asumptions standard normal distribution
3.
No,
serious violations of any other assumption plots
4.
null, H0: Ud = 0
alternate, H1: Ud > 0
test statistic: 6.371
critical value: reject Ho, if to > 1.895
decision: Reject Ho
p-value: 0.00019
5.
we have enough evidence to support the claim that if tuning a car engine would improve the gas miliage.