The Pew Research Center conducted a survey of 1020 randomly

The Pew Research Center conducted a survey of 1020 randomly selected adults and found that 85% of

them know what Twitter is. Based on that result, find the 90% confidence interval of the population

proportion of all adults who know what Twitter is. Find this interval by following the steps below:

(1 pt each) Identify for this problem:

i. The confidence level

ii. The standard error

iii. The value of the point estimate

iv. The value of the critical value

Solution

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Sample Size(n)=1020
Sample proportion = x/n =0.85
Standard Error = Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size,
Mean(x)=867
Sample Size(n)=1020
Sample proportion =0.85
Standard Error = Sqrt ( (0.85*0.15) /1020) )
= 0.0112

Confidence Interval = [ 0.85 ±Z a/2 ( Sqrt ( 0.85*0.15) /1020)]
= [ 0.85 - 1.64* Sqrt(0.0001) , 0.85 + 1.64* Sqrt(0.0001) ]
= [ 0.8317,0.8683]