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. An article reported that in one investigation, six sites along interstate highways 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:	11	23	65	117	62	66
After:	12	22	43	81	75	75

(a) The 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.]
State and test the appropriate hypotheses. (Use α = 0.05.)

H₀: μ_D = 0
H_a: μ_D ≥ 0

H₀: μ_D = 0
H_a: μ_D > 0   

H₀: μ_D = 0
H_a: μ_D ≤ 0

H₀: μ_D = 0
H_a: μ_D ≠ 0

H₀: μ_D = 0
H_a: μ_D < 0

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t value= p value=

Reject H₀. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.Fail to reject

State the conclusion in the problem context.

H₀. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.    

Fail to reject H₀. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.Reject

H₀. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.

(b) If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)

( , )

Answer 1

from above:

H₀: μ_D = 0
H_a: μ_D ≠ 0

t value= 0.771

p value=0.475

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.    

b)

for 95% CI; and 5 degree of freedom, value of t=

2.571

std error=Se=SD√(1+1/n)=

20.5848

margin of errror          =t*std error=		52.915
lower confidence limit                     =		-46.92
upper confidence limit                    =		58.92
from above 95% confidence interval for population mean =(-46.92 ,58.92)