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Q. 100

Expert-verifiedFound in: Page 553

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 $14\%$.

The adult smoking rate$=14\%$

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:

$z=\frac{{p}^{\wedge}-p}{\sqrt{\frac{p\left(1-p\right)}{n}}}\phantom{\rule{0ex}{0ex}}{P}^{\wedge}=\frac{x}{n}\phantom{\rule{0ex}{0ex}}=\frac{9}{70}\phantom{\rule{0ex}{0ex}}=0.129\phantom{\rule{0ex}{0ex}}$

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

$z=\frac{{p}^{\wedge}p}{\sqrt{\frac{p\left(1-p\right)}{n}}}\phantom{\rule{0ex}{0ex}}=\frac{-0.01143}{0.0415}\phantom{\rule{0ex}{0ex}}=0.2756$

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