Question

Throughout the 2016 Presidential election primaries, Millennials (those aged 20 to 36 years) consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the 2016 Gallup poll of 1,754 Millennials, 55% had a favorable opinion of Sanders than Hillary Clinton (38%). Calculate the 90% confidence interval for Bernie Sanders.

Answer 1

the 90% confidence interval is

`0.5305  <  p < 0.5695`

Explanation:

From the question we are told that

The sample proportion is
`\^ p = 0.55`

The sample size is n = 1754

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{( 0.55 (1- 0.55))/(1754) }`

=>
`E =  0.0195`

Generally 90% confidence interval is mathematically represented as

`\^ p -E <  p <  \^ p +E`

=>
`0.55 -0.0195 <  p < 0.55 + 0.0195`

=>
`0.5305  <  p < 0.5695`