Many freeways have service (or logo) signs that give informationon attractions, camping, lodging, food, and gas services prior tooff-ramps. These signs typically do not provide information ondistances. An article reported that in one investigation, six sitesalong interstate highways where service signs are posted wereselected. For each site, crash data was obtained for a three-yearperiod before distance information was added to the service signsand for a one-year period afterward. The number of crashes per yearbefore and after the sign changes were as follows.
| Before: | 15 | 23 | 65 | 121 | 66 | 65 |
| After: | 16 | 21 | 43 | 83 | 79 | 74 |
a)The article included the statement "A paired t testwas performed to determine whether there was any change in the meannumber of crashes before and after the addition of distanceinformation on the signs." Carry out such a test. [Note:The relevant normal probability plot shows a substantial linearpattern.]
State and test the appropriate hypotheses. (Use
? = 0.05.)
Calculate the test statistic and P-value. (Round yourtest statistic to two decimal places and your P-value tothree decimal places.)
b)If a seventh site were to be randomly selected among locationsbearing service signs, between what values would you predict thedifference in number of crashes to lie? (Use a 95% predictioninterval. Round your answers to two decimal places.)
