Age Distribution for Motor Vehicle Department

Data from the Motor Vehicle Department indicate that 80% of all licensed drivers are older than age 25.

1. In a sample of n = 60 people who recently received speeding tickets, 38 were older than 25 years and the other 22 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use α = 0.05.
2. In a sample of n = 60 people who recently received parking tickets, 43 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use α = 0.05.

(1) SOLUTION:
$$df = k-1 = 2-1 =1$$
$$f_e = 30, 30$$
$$f_o = 38, 22$$
$$\chi^2 critical$$ with df = 1 degrees of freedom at 0.05 significance level
DECISION: Since the calculated $$\chi^2$$ is greater than the critical $$\chi^2$$, we can conclude that age distribution for this sample is significantly different from the distribution for the population of licensed drivers.

(2) SOLUTION:
$$df = k-1 = 2-1 =1$$
$$f_e = 30, 30$$
$$f_o = 43, 17$$
$$\chi^2 critical$$ with df = 1 degrees of freedom at 0.05 significance level
DECISION: Since the calculated $$\chi^2$$is greater than the critical $$\chi^2$$, we can conclude that age distribution for this sample significantly different from the distribution for the population of licensed drivers.