Chapter 9.3, Problem 42E

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: 782–788) reported that in one investigation, six sites along Virginia 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:	15	26	66	115	62	64
After:	16	24	42	80	78	73

a. 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.]

 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?