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:

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?

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Before: 1526 66 115 62 64 After: 16 24 42 8078 73