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Statistics / Fundamentals of Statistics 4 / Chapter 10.4 / Problem 8AYU

Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III

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The Atomic Bomb In October 1945, the Gallup organization

Chapter 6, Problem 8AYU

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QUESTION:

The Atomic Bomb In October 1945, the Gallup organization asked 1487 randomly sampled Americans, “Do you think we can develop a way to protect ourselves from atomic bombs in case other countries tried to use them against us?” with 788 responding yes. Did a majority of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945? Use the \(\alpha=0.05\) level of significance.

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QUESTION:

The Atomic Bomb In October 1945, the Gallup organization asked 1487 randomly sampled Americans, “Do you think we can develop a way to protect ourselves from atomic bombs in case other countries tried to use them against us?” with 788 responding yes. Did a majority of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945? Use the \(\alpha=0.05\) level of significance.

ANSWER:

Answer :

Step 1

The hypotheses are ${H}_{0}$ : $p=0.5$ versus ${H}_{1}$ : $p\ >0.5$ .

Here we know that.

n = 1487; x = 788

Then

Sample proportion = $\widehat{p}$ = $\frac{x}{n}$ = $\frac{788}{1487}$ = 0.529

n ${p}_{0%7$

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