1 point) Among drivers who have had a car crash in the last year, 150 were rando

Question

1 point) Among drivers who have had a car crash in the last year, 150 were randomly selected and categorized by age, with the results listed in the table below.

If all ages have the same crash rate, we would expect (because of the age distribution of licensed drivers) the given categories to have 16%, 44%, 27%, 13% of the subjects, respectively. At the 0.05 significance level, test the claim that the distribution of crashes conforms to the distribution of ages.
The test statistic is 2=  
The conclusion is
A. There is sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.
B. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

Age Under 25 25-44 45-64 Over 64 Drivers 61 35 22 32

Explanation / Answer

Using sample data, find the degrees of freedom, expected frequency counts, test statistic, and the P-value associated with the test statistic.

Ei = npi

2 = [ (Oi - Ei)2 / Ei ]

chi-square critical = 7.82

since TS > critical value {88 > 7.82 }

we reject the null hypothesis

and conclude that

There is sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

Observed Expected =npi (Oi -Ei)^2/Ei under 25 61 24 57.04167 25-44 35 66 14.56061 45-64 22 40.5 8.450617 over 64 32 19.5 8.012821 Total 150 150 88.06571

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