This hypothesis stuff really gets at me (don\'t know why) and I\'m having troubl

Question

This hypothesis stuff really gets at me (don't know why) and I'm having trouble mastering it to applications. So thank you very much for your help.

The question:
A sample of 10 diesel trucks were run both hot and cold to estimate the difference in fuel economy. The results, in mi/gal, are presented in the following table.

Truck     Hot Cold
1 4.56 4.26
2 4.46       4.08
3 6.49       5.83
4 5.37     4.96
5 6.25       5.87
6 5.90       5.32
7 4.12       3.92
8 3.85       3.69
9 4.15       3.74
10 4.69       4.19

a) Can one conclude that the mean fuel mileage of Cold engines is less than that of the hot engines? Carry out the appropriate hypothesis test.

b) Find a 98% confidence interval for the difference in mean fuel mileage between hot and cold engines.

Any help is greatly appreciated Will rate life saver.

Explanation / Answer

Given hot: xbar1= 4.984, s1= 0.95 (based on the data)
cold: xbar2= 4.586, s2=0.84

(a) The test hypothesis is
Ho:1-2<=0
Ha:1-2>0

The test statistic is

t=(xbar1-xbar2)/[s1^2/n1 +s2^2/n2]

=(4.984-4.586)/sqrt(0.95^2/10 + 0.84^2/10)

=0.99

If a=0.05, the critical value is t(a=0.05, df=n1+n2-2=18)=1.73 (check student t table)

Since t=0.99 < 1.73, we do not reject Ho.

So we can not conclude that the mean fuel mileage of Cold engines is less than that of the hot engines

---------------------------------------------------------------------------------------------------------------------------

(b) Given a=0.02, t(0.01, df=18)=2.55(check student t table)

So 98% CI is

(xbar1-xbar2)± t*[s1^2/n1 +s2^2/n2]

--> (4.984-4.586) ± 2.55*sqrt(0.95^2/10 + 0.84^2/10)

--> ( -0.62, 1.42)

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