Question

A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2946 occupants not wearing seat belts, 31 were killed. Among 7602 occupants wearing seat belts, 16 were killed. Use a 0.01 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. H0: p1 ≤ p2
   H1: p1 ≠ p2
B. H0: p1 ≠ p2
   H1: p1 = p2
C. H0: p1 ≥ p2
   H1: p1 ≠ p2
D. H0: p1 = p2
   H1: p1 > p2
E. H0: p1 = p2
H1: p1 < p2
F. H0: p1 = p2
H1: p1 ≠ p2

Identify the test statistic.
z = _________
(Round to two decimal places as needed.)

Identify the P-value.
P-value = _________
(Round to three decimal places as needed.)

The P-value is (1) _________ the significance level of α = 0.01, so (2) _________ the null hypothesis. There (3) _________ 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 _________ < p1 − p2 < _________ .
(Round to three decimal places as needed.)

Because the confidence interval limits (4) _________ 0, it appears that the two fatality rates are (5) _________.

Because the confidence interval limits include (6) __________ values, it appears that the fatality rate is (7) _________  for those not wearing seat belts.

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

A. The results suggest that the use of seat belts is associated with the same fatality rates as 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 higher fatality rates than not using seat belts.
D. The results are inconclusive.

(1) less than
   greater than

(2) reject
   fail to reject

(3) is not
   is
(4) include
   do not include

(5) not equal.
   equal.

(6) only positive
   positive and negative
   only negative

(7) lower
   higher
   the same

Answer 1

n1= 2946, n2= 7602

x1= 31, x2= 16

a)

Ho: P1 = P2

H1: P1 > P2

Z = 5.82

P-Value = P(z < -1.95)

using normal z table we get

P(z < -1.95) = 0.0256

P-Value = 0

decision rule is

Reject Ho if ( P-value ) ( )

here, ( P-value= 0.0256 ) < ( = 0.05)

Hence, we can say,

Null hypothesis is rejected.

The P-value is (1) less han the significance level of α = 0.01, so (2) Reject the null hypothesis. There (3) is sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts.

b)

formula for confidence interval is

Where Zc is the z critical value for c=99%

Zc= 2.58

0.00339 < P1 - P2 < 0.01345

Round to three decimal places.

0.003 < P1 - P2 < 0.013

Because the confidence interval limits (4) do not include  0, it appears that the two fatality rates are (5) not equal.

Because the confidence interval limits include (6) only positive values, it appears that the fatality rate is (7)    higher for those not wearing seat belts.

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