Question

A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among 2758 occupants not wearing seat​ belts, 30 were killed. Among 7650 occupants wearing seat​ belts, 12 were killed. Use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities.

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?

Identify the test statistic. z=___

​P-value=___

The​ P-value is ____ than the significance level of α=0.05​, so ____ the null hypothesis. There ___ sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts

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

Because the confidence interval limits ___, it appears that the two fatality rates are ____. Because the confidence interval limits include ____ ​values, it appears that the fatality rate is ______ for those not wearing seat belts.

What do the results suggest about the effectiveness of seat​ belts?

Answer 1

1)

x1                =	30	x2                =	12
p̂1=x1/n1 =	0.0109	p̂2=x2/n2 =	0.0016
n1                       =	2758	n2                       =	7650
estimated prop. diff =p̂1-p̂2    =		0.0093
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.0040
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0014
test stat z=(p̂1-p̂2)/Se =		6.61
P value   =		0.0000

The​ P-value is less  than the significance level of α=0.05​, so reject the null hypothesis. There sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts

estimated difference in proportion   =p̂1-p̂2   =			0.0093
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0020
for 90 % CI value of z=		1.645
margin of error E=z*std error =		0.0033
lower bound=(p̂1-p̂2)-E=		0.0060
Upper bound=(p̂1-p̂2)+E=		0.0126
from above 90% confidence interval for difference in population proportion =(0.006 <p1-p2<0.013)

Because the confidence interval limits contain 0 it appears that the two fatality rates are different Because the confidence interval limits include all positive values   ​values, it appears that the fatality rate is higher or those not wearing seat belts