Answered: sample of 323 urban adult residents of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A sample of 323 urban adult residents of a particular state revealed 65 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 177 rural residents yielded 75 who favored the increase. Does this data indicate that the sentiment for increasing the speed limit is different for the two groups of residents?

(a) Test H₀: p₁ − p₂ = 0 versus H_a: p₁ − p₂ ≠ 0 using ? = 0.05, where p₁ refers to the urban population. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z =
P-value =

State the conclusion in the problem context.

Fail to reject H₀. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents.Reject H₀. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents. Fail to reject H₀. The data does not suggest that the sentiment for increasing the speed limit is different for the two groups of residents.Reject H₀. The data does not suggest that the sentiment for increasing the speed limit is different for the two groups of residents.

(b) If the true proportions favoring the increase are actually p₁ = 0.24 (urban) and p₂ = 0.42 (rural), what is the probability that H₀ will be rejected using a level 0.05 test with m = 323, n = 177? (Round your answer to four decimal places.)

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