Question

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

27542754

occupants not wearing seat? belts,

3535

were killed. Among

78147814

occupants wearing seat? belts,

1818

were killed. Use a

0.010.01

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 1p1less than<p 2p2

C.

Upper H 0H0?:

p 1p1equals=p 2p2

Upper H 1H1?:

p 1p1greater than>p 2p2

D.

Upper H 0H0?:

p 1p1not equals?p 2p2

Upper H 1H1?:

p 1p1equals=p 2p2

E.

Upper H 0H0?:

p 1p1equals=p 2p2

Upper H 1H1?:

p 1p1not equals?p 2p2

F.

Upper H 0H0?:

p 1p1less than or equals?p 2p2

Upper H 1H1?:

p 1p1not equals?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

less than

less than

greater than

the significance level of

alpha?equals=0.010.01?,

so

reject

fail to reject

reject

the null hypothesis. There

is

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<left parenthesis p 1 minus p 2 right parenthesisp1?p2less than<nothing.

?(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

do not include

?0, it appears that the two fatality rates are

not equal.

not equal.

equal.

Because the confidence interval limits include

only positive

only positive

only negative

positive and negative

?values, it appears that the fatality rate is

lower

higher

lower

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 higher fatality rates than not using seat belts.

B.

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

C.

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

D.

The results are inconclusive.

Click to select your answer(s).

Answer 1

a) H0 : P1 = P2

    H1 : P1 > P2

p1 = 35/2754 = 0.0127

p2 = 18/7814 = 0.0023

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

                                         = (0.0127 * 2754 + 0.0023 * 7814)/(2754 + 7814)

                                         = 0.005

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

     = sqrt(0.005 * (1 - 0.005) * (1/2754 + 1/7814))

     = 0.0016

The test statistic z = (p1 - p2)/SE

                             = (0.0127 - 0.0023)/0.0016

                             = 6.5

P-value = P(Z > 6.5)

             = 1 - P(Z < 6.5)

            = 1 - 1 = 0

The P-value is less than the significance level of alpha = 0.01, so reject the null hypothesis.

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

b) At 99% confidence interval the critical value is z_0.005 = 2.58

The confidence interval is

(p1 - p2) +/- z_0.005 * SE

= (0.0127 - 0.0023) +/- 2.58 * 0.0016

= 0.0104 +/- 0.0041

= 0.0063, 0.0145

= 0.006, 0.015

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

c) Option - B) The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts.