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A car company is considering a new engine filter for its new hybrid automobile line. But...

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Statistics

A car company is considering a new engine filter for its newhybrid automobile line. But it does not want to switch to the newbrand unless there is evidence that the new filter can improve fueleconomy for the vehicle (miles per gallon). The experimental designis 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 FilterNew Filter
17.67.3
25.17.2
310.46.8
46.910.6
55.68.8
67.98.7
75.45.7
85.78.7
95.58.9
105.37.1

Conduct a hypothesis testing to determine whether the newfiltration system is superior. Provide the p-value from youranalysis.

Answer & Explanation Solved by verified expert
4.2 Ratings (677 Votes)

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(), xÌ…d = -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.
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