Question

A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among 2997 occupants not wearing seat​ belts, 29 were killed. Among 7657 occupants wearing seat​ belts, 13 were killed. Use a 0.050 significance level to test the claim that seat belts are effective in reducing fatalities.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of occupants not wearing seat belts and the second sample to be the sample of occupants wearing seat belts. What are the null and alternative hypotheses for the hypothesis​ test?

b. Identify the test statistic.

Z=

c. Identify the​ P-value.

P-vale=

d. Test the claim by constructing an appropriate confidence interval.

The appropriate confidence interval is ___< (p1 - p2) <____

Answer 1

Ans:

a)

H0:p1<=p2

Ha:p1>p_2

b)

sample proportion for p1=29/2997=0.009676

sample proportion for p1=13/7657=0.001698

pooled proportion=(29+13)/(2997+7657)=0.0003942

Test statistic:

z=(0.009676-0.001698)/SQRT(0.003942*(1-0.003942)*((1/2997)+(1/7657)))

z=5.91

c)

p-value=P(z>5.91)=0.0000

d)

95% confidence interval for difference in proportions

=(0.009676-0.001698)+/-1.96*sqrt((0.009676*(1-0.009676)/2997)/2997)+(0.001698*(1-0.001698)/7657))

=0.0080+/-0.0036

=(0.0044, 0.0116)

confidence interval is 0.0044< (p1 - p2) <0.0116