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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

Local high school鈥檚 proportion of students who smoke is less than 0.18

Step by step solution

01

State the null and alternate hypothesis. we have to conduct hypothesis test if high school students of small city demographic take less than 18% of students have smoked, on average.

H0:p鈮�0.18;Ha:p<0.18

02

Calculate the p-value using the normal distribution for proportions: 

p-value=1

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.18), then there is a 1.0000 probability that the sample (estimated) proportion is 0.547 or more.

03

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alphadecisionreason for decision
0.05Do not reject the null hypothesis.
p-value>0.05

Conclusion: At the 5% level of significance, there is not enough evidence to conclude that the local high school鈥檚 proportion of students who smoke is less than 0.18.

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Most popular questions from this chapter

We want to test whether the mean height of eighth graders is 66inches. State the null and alternative hypotheses. Fill in the correct symbol (=,鈮�,鈮�,<,鈮�,>)for the null and alternative hypotheses.

a.H0:渭-66

b.Ha:渭-66

Suppose the null hypothesis,H0, is: the blood cultures contain no traces of pathogenX.State the TypeIand TypeIIerrors.

Previously, an organization reported that teenagers spent 4.5hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:

a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

A sleeping bag is tested to withstand temperatures of 鈥�15掳F. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.

In words, describe1鈥�尾

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use 伪 = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?
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