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:

(2 pts) List And Verify the appropriate conditions needed to calculate the intended confidence interval.

(2 pts) Calculate the confidence interval by giving the appropriate formula and then plugging numbers into that formula.(Give final interval to 3 decimal places)

(2 pts) Interpret the interval found.

(2 pts) Perform part (b) using Minitab.Give the output (what the computer prints on the screen) from Minitab here.Verify that the interval given here matched your interval in part (b).

(2 pts) What is the margin of error for your interval?How could you calculate the margin of error from ONLY the Minitab output provided in part d?

(1 pt each) Identify for this problem:

The confidence level

The standard error

The value of the point estimate

The value of the critical value

Solution

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
Mean(x)=867
Sample Size(n)=1020
Sample proportion = x/n =0.85
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]

Interpretations:
1) We are 95% sure that the interval [ 0.8317,0.8683] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contain the true population proportion

Margin of Error = 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
Mean(x)=867
Sample Size(n)=1020
Sample proportion =0.85
Margin of Error = Z a/2 * ( Sqrt ( (0.85*0.15) /1020) )
= 1.64* Sqrt(0.0001)
=0.0183