According to a recent survey, 71% of teens ages 12-17 in a certain coun d Social

Question

According to a recent survey, 71% of teens ages 12-17 in a certain coun d Social networks in 2009. A random sample of 120 teenagers us or this age group was selected. Complete parts a through d below a. Calculate the standard error of the proportion. 9" (Round to four decimal places as needed.) b. What is the probability that less than 73% of the teens from this sample used social networks? P(Less than 73% of the teens from this sample used social networks). Round to four decimal places as needed.) c, what is the probability that between 70% and 80% of the teens from this sample used social networks? P(Between 70% and 80% of the teens from this sample used social networks)- Round to four decimal places as needed.) d. What impact would changing the sample size to 200 teens have on the results of parts a b, and c? Choose the correct answer below O A. The standard error would be increased, which would, in tum, reduce the probablities that the sample proportions willbe closer to the population proportion ° C. The standard error would be increased, which would, in turn, increase the probabilities that the sample The standard error would be reduced, which would, in turn, increase the probablitios that tho sample proportions will be closer to the population proportion. error would be reduced, which would, in turn, reduce the probabilities that the sample proportions will be closer to the population proportion. E. Changing the sample size would have no effect on the standard error or the probabilities that the sample proportions will be closer to the population proportion.

Explanation / Answer

Solution:- Givwen that p = 0.71 , n = 120 , q = 1-p = 1-0.71 = 0.29

a) = sqrt(p*q/n) = sqrt(0.71*0.29/120) = 0.0414

b) P(p^ < 0.73) = P(Z < (p^ - p)/sqrt(p*q/n) )

= P(Z < (0.73 - 0.71)/ 0.0414)

= P(Z < 0.4831)

= 0.6844

c) P(0.7 < P^ < 0.8) = P((0.7 - 0.71)/ 0.0414 < Z < (0.8 - 0.71)/ 0.0414)

= P(-0.2415 < Z < 2.1739)

= 0.5798

d) option C. The standard error would be reduced, which would, in turn, increase the probabilities that the sample proportions will be closer to the population proportion

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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