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Chapter 9: Q. 104 (page 554)

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273randomly selected teen girls living in Massachusetts (between 12and 15years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

a. RejectH0: There is sufficient evidence to conclude that more than30%of teen girls smoke to stay thin.

b. Do not rejectH0: There is not sufficient evidence to conclude that less than 30%of teen girls smoke to stay thin.

c. Do not reject H0: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

d. Reject H0: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

Short Answer

Expert verified

c. Do not reject H0: There is not sufficient evidence to conclude that more than30%of teen girls smoke to stay thin.

Step by step solution

01

Given information

x=63,n=273,p0=0.30,a=0.05

02

Explanation

State the hypothesis:

The null hypothesis states that less than or equal to30%of teen girls smoke to stay thin. In symbols:

H0:p鈮�0.30

The alternative hypothesis states that more than 30%of teen girls smoke to stay thin. In symbols:

Ha:p>0.30

From the z table, the critical value of z value for the critical region is:

P铃�=xn=63273=0.231

The test statistic is:

z=p铃�-p0p01-p0n=0.231-0.300.301-0.30273=-0.0690.027735=-2.50

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

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Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter (渭orp).

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d. There is not enough evidence to conclude that the mean number of hours is more than 4.75
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