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Q. 100

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Found in: Page 553

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# 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 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.

${H}_{0}:p=0.14\phantom{\rule{0ex}{0ex}}{H}_{0}:p<0.14$

The normal distribution is:

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

The Z test statistic is:

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

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