Question

URGENT

A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among

29402940

occupants not wearing seat​ belts,

31

were killed. Among

7766

occupants wearing seat​ belts,

16

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) below.

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?

A.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

B.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

C.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

D.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

E.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than

F.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

Identify the test statistic.

zequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is

▼

greater than

less than

the significance level of

alphaαequals=0.050.05​,

so

▼

fail to reject

reject

the null hypothesis. There

▼

is not

is

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

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

The appropriate confidence interval is

nothingless than

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits

▼

do not include

include

​0, it appears that the two fatality rates are

▼

not equal.

equal.

Because the confidence interval limits include

▼

positive and negative

only negative

only positive

​values, it appears that the fatality rate is

▼

lower

higher

the same

for those not wearing seat belts.

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

A.

The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts.

B.

The results suggest that the use of seat belts is associated with the same fatality rates as not using seat belts.

C.

The results suggest that the use of seat belts is associated with higher fatality rates than not using seat belts.

D.

The results are inconclusive.

Answer 1

using excel>Addin<phstat>ywo sample test

we have

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0		of the Difference Between Two Proportions
Level of Significance	0.05
Group 1			Data
Number of Items of Interest	31		Confidence Level	95%
Sample Size	2940
Group 2			Intermediate Calculations
Number of Items of Interest	16		Z Value	-1.959963985
Sample Size	7766		Std. Error of the Diff. between two Proportions	0.001952792
			Interval Half Width	0.003827403
Intermediate Calculations
Group 1 Proportion	0.010544218		Confidence Interval
Group 2 Proportion	0.002060263		Interval Lower Limit	0.004656552
Difference in Two Proportions	0.008483955		Interval Upper Limit	0.012311358
Average Proportion	0.004390062
Z Test Statistic	5.926211873
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	1.55001E-09
Reject the null hypothesis

a. Test the claim using a hypothesis test.

the null and alternative hypotheses for the hypothesis​ test

F.

H0​:p 1=p 2

H1​:p1>p2

Identify the test statistic.

z =5.93

​P-value =0.000

What is the conclusion based on the hypothesis​ test?

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

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

The appropriate confidence interval is (0.004 ,0.012)

Because the confidence interval limits include  only positive ​values, it appears that the fatality rate is higher for those not wearing seat belts.

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

A.

The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts.