A study was conducted to determine the proportion of American teenagers between

Question

A study was conducted to determine the proportion of American teenagers between 13 and 17 who smoke. Previous surveys showed that 15% percent of all teenagers smoke. A Gallup survey interviewed a nationally representative sample of 785 teenagers aged 13 to 17. Seventy-one teenagers in the survey acknowledged having smoked at least once in the past week. Does the study provide adequate evidence to conclude that the percentage of teenagers who smoke is now different than 15%?

Be sure to answer all the questions whether or not the requirements are actually met.

Are the requirements for both a confidence interval and a hypothesis test met?

a. Yes. np10 and n(1p)10n(1-p)10, np^10, and n(1p^)10 so the requirements are met.

   b. Yes. There is a large sample n>30 so the requirements must be met.

c. No. The requirements for a confidence interval can only be met if the sample data are normally distributed.

d. No. p^<10 so the requirements for a hypothesis test are not met.

Determine the appropriate 95% confidence interval for the true proportion of teenage smokers.  Input your answers for the margin of error, lower bound and upper bound.

Determine Margin of Error for this 95% confidence interval  (Round to three decimal places). _________.

Input the lower bound. (Round to three decimal places) __________.

Input the upper bound. (Round to three decimal places) __________.

c. No. The requirements for a confidence interval can only be met if the sample data are normally distributed.

d. No. p^<10 so the requirements for a hypothesis test are not met.

Explanation / Answer

a. Yes. np10 and n(1p)10n(1-p)10, np^10, and n(1p^)10 so the requirements are met.

   b. Yes. There is a large sample n>30 so the requirements must be met

here p=71/785 =0.09

hence std error =(p(1-p)/n)1/2 =0.0102

for 95% CI. z=1.96

hence margin of error =z*std error =0.02

hence lower bound =p-margin of error =0.070

and upper boud =p+margin of error =0.111

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.