Question

In: Statistics and Probability

Over half of all American teens (ages 12 to 17 years) have an online profile, mainly...

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:

Solutions

Expert Solution

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)

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