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 20952095 passenger cars in a particular region, 239239 had only rear license plates. Among 400400 commercial trucks, 5757 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 0.100.10 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 carspassenger cars and population 2 correspond to the commercial truckscommercial trucks. Let a success be a vehicle that only has a rear license plate. A. Upper H 0H0: p 1p1equals=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 Identify the test statistic. nothing (Round to two decimal places as needed.) Identify the P-value. nothing (Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. A. RejectReject Upper H 0H0. There isis 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. Fail to rejectFail to reject Upper H 0H0. There isis 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. Fail to rejectFail to reject Upper H 0H0. There is notis 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. D. RejectReject Upper H 0H0. There is notis 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. b. Identify the confidence interval limits for the appropriate confidence interval. Let population 1 correspond to the passenger carspassenger cars and population 2 correspond to the commercial truckscommercial trucks. Let a success be a vehicle that only has a rear license plate. nothingless than

Answer #1

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = passenger cars |

p₂: proportion where Sample 2 = commercial trucks |

Difference: p₁ - p₂ |

Descriptive Statistics

Sample | N | Event | Sample p |

Sample 1 | 2095 | 239 | 0.114081 |

Sample 2 | 400 | 57 | 0.142500 |

Estimation for Difference

Difference | 90% Upper Bound for Difference |

-0.0284189 | -0.004316 |

CI based on normal approximation

Test

Null hypothesis | H₀: p₁ = p₂ |

Alternative hypothesis | H₁: p₁ < p₂ |

Method | Z-Value | P-Value |

Normal approximation | -1.51 | 0.0654 |

===================================================

Reject Ho

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