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

Question

Over half of all American teens (ages 12 to 17 years) have an online profile, mainly on Facebook. A random sample of 467 teens with profiles found that 360 included photos of themselves.

(a) Give the 99.9% large-sample confidence interval for the proportion p of all teens with profiles who include photos of themselves.
Large-sample Interval is what?

(b) Give the plus four 99.9% 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.)
Calculate the Plus four Interval:

Explanation / Answer

a) here estimated proportion= p=(x/n)=360/467=0.7709

n=467 ; therefore std error =(p(1-p)/n)1/2 =0.0194

for 99.9% CI ; z=3.2905

hence 99.9% confidence interval = p -/+ z*std error =0.7069 ; 0.8349

b) for plus 4 interval:

here estimated proportion= p=(x+2)/(n+4) =362/471=0.7686

n=467+4=471 ; therefore std error =(p(1-p)/n)1/2 =0.0194

for 99.9% CI ; z=3.2905

hence 99.9% confidence interval = p -/+ z*std error =0.7046 ; 0.8325

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