Question

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 2091 passenger cars in a particular​ region, 226 had only rear license plates. Among 375 commercial​ trucks, 56 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.

Answer 1

Using excel:

p1	0.108082
p2	0.149333
x1	226
x2	56
n1	2091
n2	375
pooled proportion	0.114355
Alpha	0.05
z critical	1.644854
test statistic	-2.31139
p value	0.010406
Standard error	0.019618
Margin of error	0.032268
Confidence interval
Lower	-0.07352
Upper	-0.00898

a)

H₀​: p1=p2

H₁​: p1<p2

z critical	1.644854
test statistic	-2.31139
p value	0.010406

P-value<alpha(0.05)

Reject the null hypothesis
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)

standard error = sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )

                        = 0.019618

margin of error = Z a/2 * (standard error)

                             =0.032268

CI = (p1-p2) ± margin of error

=(-0.07352,-0.00898)

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