Question

A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2500 occupants not wearing seat belts, 15 were killed. Among 7500 occupants wearing seat belts, 15 were killed. Use this data with 0.05 significance level to test the claim that the fatality rate is higher for those not wearing seat belts. (Write all necessary steps like Hypotheses, Test Statistic, P-value & Conclusion) Given that P(z<3.17)=0.9992.

Answer 1

SOLUTION:

From given data,

A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2500 occupants not wearing seat belts, 15 were killed. Among 7500 occupants wearing seat belts, 15 were killed. Use this data with 0.05 significance level to test the claim that the fatality rate is higher for those not wearing seat belts. (Write all necessary steps like Hypotheses, Test Statistic, P-value & Conclusion) Given that P(z<3.17)=0.9992.

Given that,

n₁ = 2500,

x₁= 15

sample proportion 1 () = x₁/n₁

= 15/2500

= 0.006

n₂ = 7500 ,

x₂ = 15

sample proportion 2( )= x₂/n₂

= 15/7500

= 0.002

The null and alternative hypotheses are,

H₀: p₁=p₂

H₁ : p₁ > p₂

Pooled proportion () is,

=   (x₁ + x₂) / (n₁ + n₂ )

= (15 +15) / (2500 + 7500 )

= 30 / 10000

= 0.003

Test statistic is,

Test statistic = Z = 3.17

since, it is right-tailed test,

p-value

P(Z > 3.17) = 1 - P(Z < 3.17)

= 1 - 0.9992

= 0.0008

p-value = 0.0008

since p =0.0008 < 0.05, it is concluded that the null hypothesis is rejected.

There is sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts.