Question

) Among drivers who have had a car crash in the last year, 170 were randomly selected and categorized by age, with the results listed in the table below. Age Under 25 25-44 45-64 Over 64 Drivers 70 41 22 37 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 p-value is 0

The conclusion is

A. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

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

Answer 1

TESTING OF HYPOTHESIS

Null hypothesis :- There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

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

the test statistics ,

calculated chi square = 227.6881

on excel we calculate tabulated value as

=> =CHIINV(Prob,df)

=CHIINV(0.025,169)

tabulated chi square= 206.8889 at 0.025 level of significance.

Decision rule :-

i) if calculated chi square > tabulated chi square then reject null hypothesis

ii)if calculated chi square < tabulated chi square then accept null hypothesis

about p value decision rule :-

i) if p value > 0.025 accept null hypothesis

ii) if p value < 0.025 reject null hypothesis

Result :- if calculated chi square(227.6881) > tabulated chi square(206.8889) then reject null hypothesis

OR   

p value(0) < 0.025 reject null hypothesis.

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