Question

Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. The article Evaluation of Adding Distance Information to Freeway-Specific Service (Logo) Signs (J. of Transp. Engr., 2011; 78-888) reported that in one investigation, six sites along Virginia interstate high ways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows:

Before: 15 26 66 115 62 64
After: 16 24 42 80 78 73
The cited article included the statement A paired t test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs. Carry out such a test. [Note: The relevant normal probability plot shows a substantial linear pattern.] a seventh site were to be randomly selected among bearing service signs, between what values predict the difference in number of crashes to lie?

Answer 1

H0 : μd = 0

H1 : μd ≠ 0

Test statistic = 0.6687 ;

Pvalue = 0.7482 ;

Fail to reject H0.

Explanation:

H0 : μd = 0

H1 : μd ≠ 0

Given the data:

Before: 15 26 66 115 62 64

After: 16 24 42 80 78 73

Difference = -1 2 24 35 -18 -9

Mean difference, d ; Σd / n

d = Σx / n = ((-1) + 2 + 24 + 35 + (-18) + (-9))

d = Σx / n = 33 / 6 = 5.5

Test statistic = (d / std / sqrt(n))

std = sample standard deviation = 20.146

Test statistic = 5.5 ÷ (20.146/sqrt(6))

Test statistic = 0.6687

The Pvalue :

P(Z < 0.6687) = 0.7482

At α = 0.05

Pvalue > α ; Hence we fail to reject H0

The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.