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Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years 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 teen girls smoke to stay thin? The alternative hypothesis is:

a.p<0.30b.p0.30c.p0.30d.p>0.30

Short Answer

Expert verified

The correct option is d.Ha:p>0.30.

Step by step solution

01

Introduction

The null hypothesis of a statistical hypothesis test always predicts that there is no impact or association between variables.

02

Explanation Part a

From the given information it is said that,

x=63

n=273

When finding the null hypothesis i.e

p=xnp=63273p=23

We can see that value of pis less than 30%, Therefore, it is not the correct option.

03

Explanation Part b

From the given information it is said that,

x=63is the number of teen girls who smoke to stay thin.

n=273is the group of teen girls randomly selected.

When finding the null hypothesis i.e

p=xnp=63273p=23

Therefore,

p0.30cannot be the correct answer as the number of girls smoking to stay thin is less than30%and here it is less than and equal to30%

04

Explanation Part c

From the given information it is said that,

x=63is the number of teen girls who smoke to stay thin.

n=273is the group of teen girls randomly selected.

When finding the null hypothesis i.e

p=xnp=63273p=23

Therefore,

p0.30cannot be the correct answer as the number of girls smoking to stay thin is less than30%and here it is greater than and equal to30%
05

Explanation Part d

As the null hypothesis states that either 30or less than 30%of girls smoke to stay thin, hence, the alternate hypothesis has to say that greater than 30%of girls smoke to stay thin. The alternate hypothesis always opposes the null hypothesis.

To calculate we are given,

x=63is the number of teen girls who smoke to stay thin.

n=273is the group of teen girls randomly selected.

p=xnp=63273p=23

23%of the girls actually smoked to stay thin. The number of girls smoking to stay thin is less than 30%.

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