Question

A tire manufacturer is interested in testing the fuel economy for two different tread patterns. Tires of each tread type were driven for 1000 miles on each of 9

different cars. The mileages, in miles per gallon, were as follows:

Car	Tread A	Tread B
1	24.7	20.4
2	22.6	19.0
3	23.9	22.4
4	26.8	23.0
5	22.4	20.8
6	23.4	23.5
7	22.6	21.3
8	19.7	18.1
9	27.3	25.8

(a) Construct an 80% confidence interval for the mean difference in fuel economy. Let d represent the mileage of tread pattern A minus the mileage of tread B. Use tables to find the critical value and round the answers to at least two decimal places.

Answer 1

Car	Tread A	Tread B	d = A - B
1	24.7	20.4	4.3
2	22.6	19.0	3.6
3	23.9	22.4	1.5
4	26.8	23	3.8
5	22.4	20.8	1.6
6	23.4	23.5	-0.1
7	22.6	21.3	1.3
8	19.7	18.1	1.6
9	27.3	25.8	1.5

The sample size is n = 9 . The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	4.3	18.49
	3.6	12.96
	1.5	2.25
	3.8	14.44
	1.6	2.56
	-0.1	0.01
	1.3	1.69
	1.6	2.56
	1.5	2.25
Sum =	19.1	57.21

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

  

The number of degrees of freedom are df = 9 - 1 = 8, and the significance level is α=0.2.

Based on the provided information, the critical t-value for α=0.2 and df = 8 degrees of freedom is t_c = 1.397

The 80% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 80 % confidence for the population mean μ is

CI = (1.45, 2.794)

which completes the calculation.