Question

1. A simple random sample of front seat occupants involved in car accidents is obtained. Among 3,281 occupants who do not wear seat belts, 60 were killed. Among 9285 occupants with seat belts, 120 were killed. Do the data provide evidence to conclude that seat belts are effective in preventing deaths? Perform a hypothesis test at the 5% significance level.

Answer 1

Answer)

Null hypothesis Ho : P1 = P2

Alternate hypothesis Ha : P1 > P2

N1 = 3281, P1 = 60/3281

N2 = 9285, P2 = 120/9285

First we need to check the conditions of normality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are greater than equal to 5 or not

N1*p1 = 60

N1*(1-p1) = 3221

N2*p2 = 120

N2*(1-p2) = 9165

All the conditions are met so we can use standard normal z table to conduct the test

Test statistics z = (P1-P2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = pooled proportion = [(p1*n1)+(p2*n2)]/[n1+n2]

After substitution

Test statistics z = 2.22

From z table, P(Z>2.22) = 0.0132

So, P-Value = 0.0132

As the obtained P-Value is less than the given significance 0.05.

We reject the null hypothesis Ho.

We have enough evidence to conclude that seat belts are effective in preventing deaths.