Question

A study examined parental influence on the decisions of teenagers from a certain large region to smoke. A randomly selected group of​ students, from the​ region, 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

263

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

53

had become established smokers. Among the

43

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

18

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

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

A prospective observational study

Your answer is correct.

An experimental study

A retrospective observational study

​b) Write the appropriate hypotheses. Let

p1

be the proportion of students whose parents disapproved of smoking who became smokers. Let

p2

be the proportion of students whose parents were lenient about smoking who became smokers.

Choose the correct answer below.

A.

H0​:

p1minus

p2equals

0

HA​:

p1minus

p2greater than

0

B.

H0​:

p1minus

p2equals

0

HA​:

p1minus

p2not equals

0

Your answer is correct.

C.

H0​:

p1minus

p2not equals

0

HA​:

p1minus

p2equals

0

D.

H0​:

p1minus

p2greater than

0

HA​:

p1minus

p2equals

0

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

A.

​No, because the Independent Groups Assumption is not satisfied.

B.

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

Your answer is correct.

C.

​No, because the​ Success/Failure Condition is not satisfied.

D.

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

E.

​No, because the Randomization Condition is not satisfied.

​d) Test the hypothesis and state the conclusion.

Determine the test statistic.

zequals

negative 3.13

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

Find the​ P-value.

Pequals

. 002

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

State the conclusion. Use a significance level of

alpha

equals0.10

.

Choose the correct answer below.

A.

Do not 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.

Reject

the null hypothesis. There

is not

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

D.

Reject

the null hypothesis. There

is

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

Your answer is correct.

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

A.

If the observed difference is the true​ difference, then there is about a

​(100 times

​P)%

chance that there is no difference in the proportions.

B.

If there is no difference in the​ proportions, there is about a

​(100 times

​P)%

chance of seeing the observed difference or larger by natural sampling variation.Your answer is correct.

C.

There is about a

​(100 times

​P)%

chance that there is no difference in the proportions.

D.

There is about a

​(100 times

​P)%

chance that there is a difference in the proportions.

​f) If that conclusion is actually​ wrong, which type of error was​ committed?

A.

A Type

II

error was committed because the null hypothesis is

false

​,

but was

not

rejected.

B.

A Type

Upper I

error was committed because the null hypothesis is

true

​,

but was

mistakenly

rejected.

Your answer is correct.

​g) Create a 90​%CI for the difference of two​ proportions,p 1 minus p 2

. I am having trouble with G.)

Answer 1

The researchers found​ that, among the

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

53: had become established smokers.

Among the 43 students who initially said their parents were lenient about​ smoking,

18 became smokers.

p1: be the proportion of students whose parents disapproved of smoking who became smokers.

p2: be the proportion of students whose parents were lenient about smoking who became smokers.

n₁ : Number of students who indicated that their parents disapproved of kids​ smoking=263

n2 :  Number students who initially said their parents were lenient about​ smoking = 43

: Sample proportion of students whose parents disapproved of smoking who became smokers =53/263 = 0.2015

: Sample proportion of students whose parents were lenient about smoking who became smokers = =18/43 = 0.4186

Formula for confidence interval for difference of two population proportions : p1-p2

: Sample Size of Sample 1	263
: Sample Size of Sample 2	43
: Sample Propotion of Sample 1	0.2015
: Sample Propotion of Sample 2	0.4186
Confidence Level	90%
(= 100-90/100=10/100 ) = 0.1	0.1
/2 (=0.1/2=0.05)	0.05
	1.6449

90% Confidence Interval for Difference in two Population proportions p₁ - p₂

90% Confidence Interval for Difference in two Population proportions p₁ - p₂ : =(-0.3474,-0.0868)