Question

An automotive researcher wanted to estimate the difference in distance required to come to a complete stop while traveling 40 miles per hour on wet versus dry pavement. Because car type plays a role, the researcher used eight different cars with the same driver and tires. The breaking distance (in feet) on both wet and dry pavement is shown in the data below. Car 1 2 3 4 5 6 7 8 Wet 107 101 109 112 105 106 111 108 Dry 72 69 74 73 76 75 78 81 a) Construct a 99% Confidence Interval for the mean difference in stopping distance between wet and dry roads. b) Test whether there is a difference in stopping distances between wet and dry roads at 1% level of significance.

Answer 1

(a)

From the given data, values of difference = d = Wet - Dry is got as follows:

Car	1	2	3	4	5	6	7	8
Wet	107	101	109	112	105	106	111	108
Dry	72	69	74	73	76	75	78	81
d = Wet - Dry	35	32	35	39	29	31	33	27

From the d values, the following statistics are calculated:

n = 8

= 32.625

s_d = 3.7773

SE = s_d/

= 3.7773/ = 1.3355

= 0.01

ndf =n - 1 = 8 - 1 = 7

From Table, critical values of t = 3.4995

Confidence interval:

32.625 (3.4995 X 1.3355)

= 32.625 4.6735

= ( 27.9515 ,37.2985)

Confidence interval:

27.9515 < < 37.2985

(b)

Test statistic is given by:

t = 32.625/1.3355 = 24.4291

Since the calculated value of t = 24.4291 is greater than critical value of t = 3.4995, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that there is significant difference in stopping distances between wet and dry roads.