Question

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.

Answer 1

could not be the same

Explanation:

Given that approximately US drivers are agewise as follows:

<25 13.2

25-45 37.7%

>45 49.1%

Observations are made for a sample of 200 fatal accidents.

Let us create hypotheses as

`H_0:  Proportions age wise are the same as for US drivers\\H_a: Proportions are different`

(Two tailed chi square test at 5% significance level)

Age <25 25-45 >45

Expected 13.2 37.7 49.1 100

Observed 42 80 78 200

Expected no 26.4 75.4 98.2 200

Chi square 9.218181818 0.280636605 4.155193483 13.65401191

df = 2

p value = 0.001084

Since p <0.05 we reject null hypothesis

At the 0.05 level, the age distribution of drivers involved in fatal accidents within the state could not be the same as the age distribution of all US drivers as there seems to be significant difference.