A study examined parental influence on the decisions ofteenagers from a certain large region to smoke. A randomly selectedgroup of? students, from the? region, who had never smoked werequestioned about their? parents' attitudes toward smoking. Thesestudents were questioned again two years later to see if they hadstarted 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 thatparental 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 ofsmoking who became smokers. Let
p2
be the proportion of students whose parents were lenient aboutsmoking 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 notsatisfied.
B.
?Yes, all of the assumptions and conditions are satisfied.
Your answer is correct.
C.
?No, because the? Success/Failure Condition is notsatisfied.
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. Choosethe correct answer below.
A.
If the observed difference is the true? difference, then thereis 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 abouta
?(100 times
?P)%
chance of seeing the observed difference or larger by naturalsampling 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 errorwas? 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 1minus p 2
. I am having trouble with G.)
