Q. 107 According to the Center for Dise... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 9: Q. 107 (page 555)

According to the Center for Disease Control website, in $2011$ at least $18 %$ of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County,KY conducted a hypothesis test at the local high school (a medium sized鈥揳pproximately $1, 200$ students鈥搒mall city demographic) to determine if the local high school鈥檚 percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the $150$ students surveyed, $82$ have smoked. Use a significance level of $0.05$ and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

Short Answer

Expert verified

There is insufficient evidence to conclude that less than $18 %$ of local high school students smoke a cigarette.

Step by step solution

Given information

$x = 82, n = 150, p_{0} = 0.18, a = 0.05$

Explanation

State the hypothesis:

The null hypothesis states that at least $18 %$ of local high school students smoke cigarettes. In symbols:

$H_{0} : p 鈮� 0.18$

The alternative hypothesis states that less than $18 %$ of local high school students smoke a cigarette. In symbols:

$H_{a} : p < 0.18$

The sample proportion is:

$\overset{铃�}{P} = \frac{x}{n} = \frac{82}{150} = 0.547$

The test statistic is:

$z = \frac{\overset{铃�}{p} - p_{0}}{\sqrt{\frac{p_{0} (1 - p_{0})}{n}}} = \frac{0.547 - 0.18}{\sqrt{\frac{0.18 (1 - 0.18)}{150}}} = \frac{0.367}{0.03137} = 11.69$

For the left tailed test, the p-value is:

$p - v a l u e = P (z < 11.69) = 1.0000$

Since the null hypothesis is not rejected, there is insufficient evidence to conclude that more $30 %$ of teen girls smoke to stay thin.

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