Question

1. Approximately 13.2% of US drivers are younger than age 25, with 37.7% in the 25-44 age group, and 49.1% in the 45-and-over-category. For a random sample of 200 fatal accidents in her state, a safety expert finds that 42 drivers were under 25 years old, 80 were 25-44 years old, and 78 were at least 45 years old. At the 0.05 level, test whether the age distribution of drivers involved in fatal accidents within the state could be the same as the age distribution of all US drivers. Define H0 : Define H1 : Distribution of All US Drivers by Age - Census Data <25 25-44 45+ 13.2% 37.7% 49.1% Data for Fatal Accident Victims - Observed from Sample <25 25-44 45+ Data for Fatal Accident Victims - Expected <25 25-44 45+ Calculated χ2 Degrees of Freedom Critical χ2 Reject H0 or not? Are distributions the same or different?

Answer 1

Age	Observed (O)	Expected (E)	(O - E)^2/E
< 25	42	26.4	9.2182
25 - 44	80	75.4	0.2806
45+	78	98.2	4.1552
		χ2 =	13.6540
		Df = 2
		Critical χ2 =	5.9915

Since 13.6540 > 5.9915, we reject Ho

There is sufficient evidence that the distributions are different.