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In: Statistics and Probability

A study examined parental influence on​ teenagers' decisions to smoke. A group of students who had...

A study examined parental influence on​ teenagers' decisions to smoke. A group of students who had never smoked were questioned about their​ parents' attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found​ that, among the

284

students who indicated that their parents disapproved of kids​ smoking,

64

had become established smokers. Among the

30

students who initially said their parents were lenient about​ smoking,

12

became smokers. Do these data provide strong evidence that parental attitude influences​ teenagers' decisions about​ smoking? Complete parts a through f.

​a) What kind of design did the researchers​ use?

A retrospective observational study

An experiment

A prospective observational study

​b) Write the appropriate hypotheses. Let

p1

be the proportion of teenagers whose parents had indicated disapproval of smoking for them who became smokers themselves. Let

p2

be the proportion of teenagers whose parents had expressed leniency toward smoking for them who became smokers themselves. Choose the correct answer below.

A.

H0​:

p1minus

p2not equals

0

HA​:

p1minus

p2equals

0

B.

H0​:

p1minus

p2equals

0

HA​:

p1minus

p2not equals

0

C.

H0​:

p1minus

p2equals

0

HA​:

p1minus

p2greater than

0

D.

H0​:

p1minus

p2greater than

0

HA​:

p1minus

p2equals

0

​c) Are the assumptions and conditions necessary for inference​ satisfied?

A.

​Yes, all of the assumptions and conditions are satisfied.

B.

​No, because the randomization condition is not satisfied.

C.

​No, because the​ 10% condition is not satisfied.

D.

​No, because the​ success/failure condition is not satisfied.

E.

​No, because the independent groups assumption is not satisfied.

​d) Test the hypothesis and state your conclusion.

Determine the test statistic.

zequals

nothing

​(Round to two decimal places as​ needed.)

Find the​ P-value.

Pequals

nothing

​(Round to four decimal places as​ needed.)

State your conclusion. Use a significance level of

alpha

equals0.05

.

Choose the correct answer below.

A.

Reject

the null hypothesis. There

is

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

B.

Do not reject

the null hypothesis. There

is not

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

C.

Do not reject

the null hypothesis. There

is

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

D.

Reject

the null hypothesis. There

is not

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

​e) Explain in this context what your​ P-value means. Choose the correct answer below.

A.

If there is no difference in the​ proportions, there is about a​ (100P)% chance of seeing the observed difference or larger by natural sampling variation.

B.

There is about a​ (100P)% chance that there is a difference in the proportions.

C.

There is about a​ (100P)% chance that there is no difference in the proportions.

D.

If the observed difference is the true​ difference, then there is about a​ (100P)% chance that there is no difference in the proportions.

​f) If that conclusion is actually​ wrong, which type of error did you​ commit?

Type

Upper I

error

Type

II

error

Solutions

Expert Solution

orchestra answered 2 years ago
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