Question

A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among 2850 occupants not wearing seat​ belts, 34 were killed. Among 7617 occupants wearing seat​ belts, 15 were killed. Use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts​ (a) through​ (c).

Answer 1

Null hypothesis: There is no effect of wearing seat belts in reducing fatalities of front seat occupants in the car crashes or Proportion of occupants who died wearing seat belts (p1) Proportion of occupants who died not wearing seat belts (p2)

Alternative hypothesis: Wearing Seat belts is effective in reducing fatalities or p1> p2

Here p1 = 15/7617 = 0.002

p2 = 34/2850 = 0.012

n1 = 7617

n2 = 2850

So pooled proportion (pc) = (15+44)/(7617+2850) = 0.006

Now test statistic z is given by

= (0.002- 0.012)/0.0017

= -5.88

Critical value of z at 0.05 significance level is

z critical = 1.96

Since magnitude of the calculated z is greater than the critical z, we will reject the null hypothesis. Hence wearing seat belts is effective in reducing fatalities.