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Chapter 9: Q. 107 (page 555)

According to the Center for Disease Control website, in 2011 at least18%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–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the150 students surveyed, 82have 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 than18%of local high school students smoke a cigarette.

Step by step solution

01

Given information

x=82,n=150,p0=0.18,a=0.05

02

Explanation

State the hypothesis:

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

H0:p≥0.18

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

Ha:p<0.18

The sample proportion is:

P⏜=xn=82150=0.547

The test statistic is:

z=p⏜-p0p01-p0n=0.547-0.180.181-0.18150=0.3670.03137=11.69

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

p-value=Pz<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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Most popular questions from this chapter

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