Question

Over half of all American teens (ages 12 to 17 years) have an online profile, mainly on Facebook. A random sample of 471 teens with profiles found that 301 included photos of themselves. (a) Give the 90% large-sample confidence interval for the proportion p of all teens with profiles who include photos of themselves. Large-sample Interval:

(b) Give the plus four 90% confidence interval for p . (The plus-four interval always pulls the results away from 0% or 100%, whichever is closer. Even though the condition for using the large-sample interval is met, the plus four interval is more trustworthy.) Plus four Interval:

Answer 1

a)

sample success x =		301
sample size n=		471.0
pt estiamte p̂ =x/n=		0.6391
se= √(p*(1-p)/n) =		0.0221
for 90 % CI value of z=		1.645
margin of error E=z*std error   =		0.0364
lower bound=p̂ -E                       =		0.6027
Upper bound=p̂ +E                     =		0.6755
from above 90% confidence interval for population proportion =(0.6027 ,0.6755)

b)

or plus four interval ; add 2 in success and 4 in sample size:

sample success x =		303
sample size n=		475.0
pt estiamte p̂ =x/n=		0.6379
se= √(p*(1-p)/n) =		0.0221
for 90 % CI value of z=		1.645
margin of error E=z*std error   =		0.0363
lower bound=p̂ -E                       =		0.6016
Upper bound=p̂ +E                     =		0.6742
90% confidence interval for population proportion =(0.6016 , 0.6742)