Question

YThe Pew Research Center conducted a survey of 1007 adults and found that 85% of them know what Twitter is. Find a 90% confidence interval for the proportion of all adults who know what Twitter is. Also find the margin of error. Round all of your answers to four decimal places.

Answer 1

The 90% confidence interval is
`0.8315 <  p < 0.8685`

Explanation:

From the question we are told that

The sample size is n = 1007

The sample proportion is
`\^ p = 0.85`

From the question we are told the confidence level is 90% , hence the level of significance is

`\alpha = (100 - 90 ) \%`

=>
`\alpha = 0.10`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.645`

Generally the margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } * \sqrt{(\^ p(1- \^ p))/(n)}`

=>
`E =1.645 * \sqrt{(0.85 (1- 0.85 ))/(1007)}`

=>
`E = 0.0185`

Generally 90% confidence interval is mathematically represented as

`\^ p -E <  p <  \^ p +E`

=>
`0.85 -0.0185 <  p < 0.85 + 0.0185`

=>
`0.8315 <  p < 0.8685`