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Name: Test the given claim. Identify the null hypothesis, alternative hypoth
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Description: 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 2010 passenger cars

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 2010 passenger cars in a particular region, 234 had only rear license plates. Among 314 commercial trucks, 46 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 0.10 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<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

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

Identify the P-value.

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 sufficent evidence to support the claim that commericial trucks owners violate laws requriing front license plates at a higher rate than owners of passenger cars.

B. Fail to reject H0. There is not sufficent evidence to support the claim that commericial trucks owners violate laws requriing front license plates at a higher rate than owners of passenger cars.

C. Reject H0. There is not sufficent evidence to support the claim that commericial trucks owners violate laws requriing front license plates at a higher rate than owners of passenger cars.

D. Reject H0. There is sufficent evidence to support the claim that commericial trucks owners violate laws requriing front license plates at a higher rate than owners of passenger cars.

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.

__ < p1 - p2 < __ (Round to four decimals places as needed)

Because the confidence interval limits ____ (contain or do not contain)

there ___ (is or is not) a significant difference between the two proportions. There __ (is not or 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.

Expert Solution

Step 1

Given Information:

Sample size ( $n_{1}$ ) = 2010

Out of which $x_{1} =$ 234 passenger cars had only rear license plates.

Sample size ( $n_{2}$ ) = 314

Out of which $x_{2} =$ 46 commercial trucks had only rear license plates.

Significance level $α = 0.10$

Claim: commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

(a) State the hypothesis as follows:

Let $p_{1}$ denote the population proportion of passenger cars and $p_{2}$ denote the population proportion of commercial trucks.

Null Hypothesis $H_{0} : p_{1} = p_{2}$

Alternative Hypothesis $H_{1} : p_{1} < p_{2}$ (claim) That is, passenger car owners violate laws at a lower rate than owners of commercial trucks.

Correct option is (C)

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