Question

4. Listed below are the combined city – highway fuel consumption ratings (in miles per gallons) for different cars measured in old rating system and cars in a new rating system introduced in 2008 (based on data from USA today). A. Construct a 90 percent confidence interval of the difference in the ratings of cars. (Use 3 decimal places) (10 pts) Old Rating: 16 18 27 17 33 28 33 18 24 19 18 27 22 18 20 29 19 27 20 21 New Rating: 15 16 24 15 29 25 29 16 22 17 16 24 20 16 18 26 17 25 18 19 B. Based on the interval is there a reason to believe that there is a difference in the ratings of the two cars? C. Is there any significant difference in the old and new ratings of cars? Use appropriate hypothesis test to answer this question.

Answer 1

the 90% confidence interval for difference between old and new ratings

where

=5.0543

degrees of freedom = n1+n2 -2 = 20+20-2=38

For 90% confidence ( 0.10) with df= 38 , two tailed critical value of t is

tc = 1.69 (from t table)

Thus 90% confidence interval is

= ( -0.35 , 5.05)

B) As 90% confidence interval for difference in mean rating contains 0 , there is not sufficient evidence to conclude that there is difference in mean ratings of two cars .

Note : as confidence interval include 0 , there is possibility of true mean difference being zero .

C)

The null and alternative hypothesis

Test statistic

= 1.47

For 0.10 with df= 38 , two tailed critical value of t is

tc = 1.69 (from t table)

Since calculated t < 1.69

We fail to reject the null hypothesis

there is not sufficient evidence to conclude that there is difference in mean ratings of two cars .

	x1	(x1-x1bar)^2			x2	(x2-x2bar)^2
	16	44.89			15	28.6225
	18	22.09			16	18.9225
	27	18.49			24	13.3225
	17	32.49			15	28.6225
	33	106.09		1287	29	74.8225
	28	28.09			25	21.6225
	33	106.09			29	74.8225
	18	22.09			16	18.9225
	24	1.69			22	2.7225
	19	13.69			17	11.2225
	18	22.09			16	18.9225
	27	18.49			24	13.3225
	22	0.49			20	0.1225
	18	22.09			16	18.9225
	20	7.29			18	5.5225
	29	39.69			26	31.9225
	19	13.69			17	11.2225
	27	18.49			25	21.6225
	20	7.29			18	5.5225
	21	2.89			19	1.8225
sum/ss	454	548.2		sum/ss	407	422.55
mean =sum/20	22.7			mean =sum/20	20.35
s^2=ss/19		28.85263158		s^2=ss/19		22.23947368
s		5.371464566		s		4.715874647