Using the data set 11.2.14, test the claim that the time it takes to rent a car
ID: 3149966 • Letter: U
Question
Using the data set 11.2.14, test the claim that the time it takes to rent a car from Thrifty is the same as renting from Hertz. Conduct the test at the alpha 0.05 level of significance.
Thrifty Hertz
Chicago 21.81 18.99
Los Angeles 29.89 48.99
Houston 17.9 19.99
Orlando 27.98 35.99
Boston 24.61 25.6
Seattle 21.96 22.99
Pittsburgh 20.9 19.99
Phoenix 47.75 36.99
New Orleans 33.81 26.99
Minneapolis 33.49 20.99
Explanation / Answer
Let ud = u2 - u1.
The differences are
-2.82
19.1
2.09
8.01
0.99
1.03
-0.91
-10.76
-6.82
-12.5
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the standard deviation of the differences (third column):
s = 8.32379225
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 2.632214228
Calculating the mean of the differences (third column):
XD = -0.259
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = -0.098396246
As df = n - 1 = 9
Then the critical value of t is
tcrit = +/- 2.262157163
Also, using p values,
p = 0.923774291
As |t| < 2.262, and P > 0.05, WE FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that the time it takes to rent a car from Thrifty is not the same as renting from Hertz at 0.05 level. [CONCLUSION]
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