Question

The Center for Internet & Society at Harvard recently conducted a study analyzing the privacy management habits of teen internet users. In a group of 50 teens, 13 reported having more than 500 friends on Face-book. Use the “plus four” method to find a 90% confidence interval for the true proportion of teens who would report having more than 500 Face-book friends.

What is the size of the sample n:

What is the number of students reported having friends x =

What is the confidence level?

What is the  αvalue?

What is the   α2value?

What is the point estimate of the population proportion  ρ′(true proportion)

What is the false proportion q'

What is the confidence interval ? (p′ – EPB, p′ + EPB)

Answer 1

TRADITIONAL METHOD
given that,
possible chances (x)=13
sample size(n)=50
success rate ( p )= x/n = 0.26
I.
sample proportion = 0.26
standard error = Sqrt ( (0.26*0.74) /50) )
= 0.062
II.
margin of error = Z a/2 * (standard error)
where,
Za/2 = Z-table value
level of significance, α = 0.1
from standard normal table, two tailed z α/2 =1.645
margin of error = 1.645 * 0.062
= 0.102
III.
CI = [ p ± margin of error ]
confidence interval = [0.26 ± 0.102]
= [ 0.158 , 0.362]
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DIRECT METHOD
given that,
possible chances (x)=13
sample size(n)=50
success rate ( p )= x/n = 0.26
CI = confidence interval
confidence interval = [ 0.26 ± 1.645 * Sqrt ( (0.26*0.74) /50) ) ]
= [0.26 - 1.645 * Sqrt ( (0.26*0.74) /50) , 0.26 + 1.645 * Sqrt ( (0.26*0.74) /50) ]
= [0.158 , 0.362]
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interpretations:
1. We are 90% sure that the interval [ 0.158 , 0.362] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
90% sure that the interval [ 0.158 , 0.362] the true proportion of teens who would report having more than 500 Face-book friends.