Homework SourseA federal regulatory agency is investigating an advertised c
A federal regulatory agency is investigating an advertised claim that a certain device can increase the gasoline mileage of cars (mpg). Ten such devices are purchased and installed in cars belonging to the agency. Gasoline mileage for each of the cars is recorded both before and after installation. The data are recorded here.
x
(a) The cars in the study appear to have grossly different mileages before the devices were installed. Use the change data to test whether there has been a significant gain in mileage after the devices were installed. Use ? = .05.
B) Construct a 90% confidence interval for the mean change in mileage. On the basis of this interval, can one reject the hypothesis that the mean change is either zero or negative? (Note that the two-sided 90% confidence interval corresponds to a one-tailed ? = .05 test by using the decision rule: reject H0: ? ? ?0 if ?0 is greater than the upper limit of the confidence interval.)
| Car | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | n | x | s | |
| Before (mpg) | 19.1 | 29.9 | 17.6 | 20.2 | 23.5 | 26.8 | 21.7 | 25.7 | 19.5 | 28.2 | 10 | 23.22 | 4.25 |
| After (mpg) | 25.8 | 23.7 | 28.7 | 25.4 | 32.8 | 19.2 | 29.6 | 22.3 | 25.7 | 20.1 | 10 | 25.33 | 4.25 |
| Change (mpg) | 6.7 | ?6.2 | 11.1 | 5.2 | 9.3 | ?7.6 | 7.9 | ?3.4 | 6.2 | ?8.1 | 10 | 2.11 | 7.54 |
Solution
(a) H0: ?after = before
Ha: ?after>before
t= mean difference/(s/vn)
=-0.885
p-value= 0.1995
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(b)
| 23.2200 | mean Before (mpg) | |||
| 25.3300 | mean After (mpg) | |||
| -2.1100 | mean difference (Before (mpg) - After (mpg)) | |||
| 7.5375 | std. dev. | |||
| 2.3836 | std. error | |||
| 10 | n | |||
| 9 | df |
