A press release states that "by an overwhelming margin, Americans want to live in a sunny place." This statement is based on data from a nationally representative sample of 2260 adult Americans. Of those surveyed, 1255 indicated that they would prefer to live in a hot climate rather than a cold climate. Suppose that you want to determine if there is convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate. (Suppose p = proportion of all adult Americans who would prefer to live in a hot climate rather than a cold climate) (a) What hypotheses should be tested to answer this question? H0: p = 0.5 versus Ha: p > 0.5 H0: p = 0.5 versus Ha: p < 0.5 H0: p ≠ 0.5 versus Ha: p = 0.5 H0: p < 0.5 versus Ha: p > 0.5 H0: p = 0.5 versus Ha: p ≠ 0.5 (b) The P-value for this test is 0.00000007. What conclusion would you reach if ? = 0.01? Fail to reject H0. We have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate.Reject H0. We do not have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate. Reject H0. We have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate.Fail to reject H0. We do not have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate.

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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Question

A press release states that "by an overwhelming margin, Americans want to live in a sunny place." This statement is based on data from a nationally representative sample of 2260 adult Americans. Of those surveyed, 1255 indicated that they would prefer to live in a hot climate rather than a cold climate.

Suppose that you want to determine if there is convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate. (Suppose p = proportion of all adult Americans who would prefer to live in a hot climate rather than a cold climate)

(a)

What hypotheses should be tested to answer this question?

H₀: p = 0.5

versus

H_a: p > 0.5

H₀: p = 0.5

versus

H_a: p < 0.5

H₀: p ≠ 0.5

versus

H_a: p = 0.5

H₀: p < 0.5

versus

H_a: p > 0.5

H₀: p = 0.5

versus

H_a: p ≠ 0.5

(b)

The P-value for this test is 0.00000007. What conclusion would you reach if ? = 0.01?

Fail to reject H₀. We have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate.Reject H₀. We do not have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate. Reject H₀. We have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate.Fail to reject H₀. We do not have convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate.

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