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Q. 100

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Introductory Statistics

Found in: Page 553

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

According to an article in Bloomberg Businessweek, New York City's most recent adult smoking rate is $14 % .$ Suppose that a survey is conducted to determine this year’s rate. Nine out of $70$ randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still $14 %$ or if it has decreased.

The hypothesis test has resulted in a p-value greater than the alpha value and the null hypothesis is not rejected and the rate is still at $14 %$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

The adult smoking rate $= 14 %$

Step 2: Explanation

State the hypothesis:

The null hypothesis states that $14 %$ of adults do smoke and the alternate hypothesis states that not more than $14 %$ of adults do smoke.

$H_{0} : p = 0.14 H_{0} : p < 0.14$

The normal distribution is:

$N (0.14, \sqrt{\frac{(0.14) (0.86)}{70}})$

The Z test statistic is:

$z = \frac{p^{\land} - p}{\sqrt{\frac{p (1 - p)}{n}}} P^{\land} = \frac{x}{n} = \frac{9}{70} = 0.129$

Substitute the $p^{\land}$ value in the Z statistic formula

$z = \frac{p^{\land} p}{\sqrt{\frac{p (1 - p)}{n}}} = \frac{- 0.01143}{0.0415} = 0.2756$

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