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25 Nov

# 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: 14 22 64 122 60 63
After: 15 21 41 84 75 72
(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 =0.05.)

Calculate the test statistic and $P$-value. (Round your test statistic to two decimal places and your $P$-value to three decimal places.)
t = ________
P-value = ________
State the conclusion in the problem context.
Reject . The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
Reject . 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 . 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 . 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.)
(_______, _______)

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: 14 22 64 122 60 63

After: 15 21 41 84 75 72

(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 =0.05.)

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

t = ________

P-value = ________

State the conclusion in the problem context.

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

Reject . 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 . 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 . 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.)

(_______, _______)