Question

on a Ti calculator

(2 points) Among drivers who have had a car crash in the last year, 230 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 92 57 31 50 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 x2 = The conclusion is O A. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages. O 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

distributions of ages.

Given : drivers (observed value) 92 age under 25 25-44 45-64 over 64 57 Expected values 230 X 0.16 = 36.8 230 X 0.44 = 101.2 230 X 0.27 = 62.1 230 X 0.13 = 29.9 31 50 2.30 To test : Ho: p=0.16; P2 = 0.44 P3=0.27: by = 0.13 H some of the population proportions differ from the value stated in the null hypothesis Test statistic 22 E (01-€;) C92-36-8)2 368 (57-101-2)2 101.2 (31-62.1) 62.1 (50 - 29.9) 29.9 X S 82.8 + 19.305 + IS S75 + 13. 512 X: 131. 192 x critical at X=0.025, df = n-1 : 4-13 Xcritical = 9.348 (from chi-square table) Here, x² > X² critical, We reject Ho. There is suffictent evidence to odrrant the rejection of the claim that the distribution of crashes conforms to the