Question

A car company is considering a new engine filter for its new hybrid automobile line. But it does not want to switch to the new brand unless there is evidence that the new filter can improve fuel economy for the vehicle (miles per gallon). The experimental design is set up so that each of the 10 cars drive the same course twice - once with the old filtration system and once with the new version. The data collected is shown below:

Car #	Current Filter	New Filter
1	7.6	7.3
2	5.1	7.2
3	10.4	6.8
4	6.9	10.6
5	5.6	8.8
6	7.9	8.7
7	5.4	5.7
8	5.7	8.7
9	5.5	8.9
10	5.3	7.1

Conduct a hypothesis testing to determine whether the new filtration system is superior. Provide the p-value from your analysis.

Answer 1

Current Filter	New Filter	Difference
7.6	7.3	0.3
5.1	7.2	-2.1
10.4	6.8	3.6
6.9	10.6	-3.7
5.6	8.8	-3.2
7.9	8.7	-0.8
5.4	5.7	-0.3
5.7	8.7	-3
5.5	8.9	-3.4
5.3	7.1	-1.8

Sample mean of the difference using excel function AVERAGE(), x̅d = -1.4400

Sample standard deviation of the difference using excel function STDEV.S() sd = 2.2406

Sample size, n = 10

Null and Alternative hypothesis:  

Ho : µd =    0

H1 : µd <    0

Test statistic:  

t = (x̅d)/(sd/√n) = (-1.44)/(2.2406/√10) =    -2.0323

df = n-1 =    9

p-value :  

Left tailed p-value = T.DIST(-2.0323, 9, 1) =    0.0363

Decision:  

p-value < 0.05, Reject the null hypothesis  

Conclusion:  

There is enough evidence to conclude that  the new filtration system is superior at 0.05 significance level.