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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 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鈮�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铃�=xn=82150=0.547

The test statistic is:

z=p铃�-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

Determine both TypeIand TypeIIerrors for the following scenario:

Assume a null hypothesis,H0, that states the percentage of adults with jobs is at least 88%.

Identify the TypeIand Type IIerrors from these four statements.

a. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88%when that percentage is actually less than 88%

b. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88%when the percentage is actually at least 88%.

c. Reject the null hypothesis that the percentage of adults who have jobs is at least 88%when the percentage is actually at least 88%.

d. Reject the null hypothesis that the percentage of adults who have jobs is at least 88%when that percentage is actually less than 88%.

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

a. Is this a test of one mean or proportion?

b. State the null and alternative hypotheses.

H0:

Ha:

c. Is this a right-tailed, left-tailed, or two-tailed test?

d. What symbol represents the random variable for this test?

e. In words, define the random variable for this test.

f. Calculate the following:

i.x=

ii.role="math" localid="1649760873126" n=

iii.p'=

g. Calculate role="math" localid="1649760901479" 蟽x=Show the formula set-up.

h. State the distribution to use for the hypothesis test.

i. Find the p-value.

j. At a pre-conceived 伪=0.05, what is your:

i. Decision:

ii. Reason for the decision:

iii. Conclusion (write out in a complete sentence):

According to the N.Y. Times Almanac the mean family size in the U.S. is 3.18. A sample of a college math class resulted in the following family sizes:

5;4;5;4;4;3;6;4;3;3;5;5;6;3;3;2;7;4;5;2;2;2;3;2

At 伪=0.05 level, is the class鈥� mean family size greater than the national average? Does the Almanac result remain valid? Why?

H0: 渭 = 10, Ha: 渭 < 10 Assume the p-value is 0.0935. What type of test is this? Draw the picture of the p-value.

Assume the null hypothesis states that the mean is equal to 88. The alternative hypothesis states that the mean is not

equal to 88. Is this a left-tailed, right-tailed, or two-tailed test?
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