Among drivers who have had a car crash in the last year, 130 were randomly selec

Question

Among drivers who have had a car crash in the last year, 130 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 0.025 significance level, test the claim that the distribution of crashes conforms to the distribution of ages.
The test statistic is 2=  
The critical value 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.

Explanation / Answer

> observed=c(49,32,18,31)
> expected=c(0.16,0.44,0.27,0.13)
> chisq.test(x=observed,p=expected)

Chi-squared test for given probabilities

data: observed
X-squared = 69.429, df = 3, p-value = 5.655e-15

Test statistic : X2 = 69.429
Critical value : Upper 2.5%point of chi-square distribution with df 3 = 9.348404
Since Test statistic > critical value, hence
A. There is sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

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