Question

# 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 273 students who indicated that their parents disapproved of kids​ smoking, 71 had become established smokers. Among the 35 students who initially said their parents were lenient about​ smoking, 15 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?

An experiment

A retrospective observational study

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​: p1minusp2not equals0 HA​: p1minusp2equals0

B. H0​: p1minusp2greater than0 HA​: p1minusp2equals0

C. H0​: p1minusp2equals0 HA​: p1minusp2not equals0

D. H0​: p1minusp2equals0 HA​: p1minusp2greater than0

​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​ success/failure condition is not satisfied.

D. ​No, because the​ 10% 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. z=? nothing ​(Round to two decimal places as​ needed.) Find the​ P-value. P=? nothing ​(Round to four decimal places as​ needed.)

State your conclusion. Use a significance level of alphaequals0.05. 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. Reject the null hypothesis. There is 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. Do not reject the null hypothesis. There is not sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

(a) A prospective observational study.
(c) ​Yes, all of the assumptions and conditions are satisfied.
(d) State your conclusion. Reject the null hypothesis. There is sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.