Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Among
2166
passenger cars in a particular region,
233
had only rear license plates. Among
379
commercial trucks,
58
had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a
0.05
significance level to test that hypothesis.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
a. Identify the null and alternative hypotheses for this test. Let population 1 correspond to the
passenger cars
and population 2 correspond to the
commercial trucks.
Let a success be a vehicle that only has a rear license plate.
A.
H0:
p1
H1:
p1=p2
B.
H0:
p1=p2
H1:
p1
C.
H0:
p1=p2
H1:
p1≠p2
D.
H0:
p1=p2
H1:
p1>p2
Part 2
Identify the test statistic.
(Round to two decimal places as needed.)
Part 3
Identify the P-value.
(Round to three decimal places as needed.)
Part 4
State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
A.
Fail to reject
H0.
There
is
sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
B.
Reject
H0.
There
is not
sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
C.
Reject
H0.
There
is
sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
D.
Fail to reject
H0.
There
is not
sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
Part 5
b. Identify the confidence interval limits for the appropriate confidence interval. Let population 1 correspond to the
passenger cars
and population 2 correspond to the
commercial trucks.
Let a success be a vehicle that only has a rear license plate.
( )
(Round to four decimal places as needed.)
Part 6
Because the confidence interval limits
[ contain ; do not contain ]
0, there
[ is ; is not ]
a significant difference between the two proportions. There
[ is ; is not ]
sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
