Question

In survey conducted by Quinnipiac University from October 25-31, 2011, 47% of a sample of 2,294 registered voters approved of the job Barack Obama was doing as president. What is the 99% confidence interval for the proportion of all registered voters who approved of the job Barack Obama was doing as president?

Answer 1

Confidence interval = [ 0.4432, 0.4968]

Explanation:

Registered voters approved of the job Barack Obama was doing as president,

p = 47% = 0.47

Total sample size, n = 2,294

Confidence level = 99%

now,

confidence interval for the proportion of all registered voters who approved of the job Barack Obama was doing as president

= p ±
`z*\sqrt{(p*(1-p))/(n)}`

for 99% confidence level, z value is 2.58

= 0.47 ±
`2.58*\sqrt{(0.47*(1-0.47))/(2294)}`

= 0.47 ± 0.0268

or

Confidence interval = [0.47 - 0.0268, 0.47 + 0.0268 ]

or

Confidence interval = [ 0.4432, 0.4968]