All problems are to show check of assumptions first, and have complete 7 step hy
ID: 3066771 • Letter: A
Question
All problems are to show check of assumptions first, and have complete 7 step hypothesis tests.
1) Automobile companies are working diligently to reduce gasoline consumption in their new automobiles. A random sample of 15 different models of cars was selected from each country and tested for how many miles per gallon each car achieved. The data are normally distributed and the variances of the two sets of data may be assumed to be equal so no check of assumptions is necessary. Are Japanese auto companies doing better at reducing gasoline consumption when compared to US companies? Use an appropriate level of significance for this study.
US = mpg for US cars, JA = mpg for Japanese cars
- US 18 15 23 26 22 14 21 29 13 14 19 23 24 25 16
- JA 23 28 32 24 27 24 21 20 33 36 26 27 26 24 25
Explanation / Answer
Below are the null and alternate hypothesis
H0: mu(us) - mu(ja) >= 0
H1: mu(us) - mu(ja) < 0
from the given data
As it is given that variances of two sets are equal, we use pooled t-test
Pooled estimate of variance
Sp = sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2))
Sp = 4.7031
DF = 15 + 15 - 2 = 28
SE = 4.7031 * sqrt(1/15+1/15) =1.7173
Test statistics, t = (20.1333 - 26.4)/1.7173 = -3.6492
p-value = 0.0005
As p-value is less than the significance level of 0.05, we reject the null hypothesis.
This means there are significant evidence to conclude that Japenese auto companies are doing better at reducing gasoline consumption when compared to US companies.
n1 15 n2 15 x1bar 20.1333 x2bar 26.4000 sigma1 (s1) 4.9838 sigma2 (s2) 4.4045