Question

A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the accompanying table. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample​ data?

	0	1-14	15-34	35 and over
Wear Seat Belts	195	19	45	11
Don't Wear Seat Belts	153	11	30	12

A. Determine the null and alternative hypotheses.

B. Find the chi squared χ2 test​ statistic

C. Find P value

Answer 1

(A) We have to test whether the amount of smoking is independent of seat belt use. So, the null and alternate hypotheses for the test are

Ho: Amount of smoking is independent of seat belt use

H1: Amount of smoking is not independent of seat belt use

(B) Using TI 84 calculator

Press 2nd, then MATRIX, select EDIT and enter the data into matrix A

Again, press STAT then TESTS and select

Observed = [A]

Expected = [B]

Calculate

We get

Test statistic = 1.671

p-value = 0.643

df = 3

(c) p value = 0.643 (From TI 84 result)

Since the p value is greater than significance level 0.05, so the theory is not supported by data.