Question

Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years) consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the 2016 Gallup poll of 1,754 Millenials, 55% had a favorable opinion of Sanders than Hillary Clinton (38%). Calculate the 90% confidence interval for Bernie Sanders. *round to two decimals (Please read the rules for rounding in the preface page xvi. If the number you are rounding is followed by 5, 6, 7, 8, 9 round the number up. If the number is followed by 0,1,2,3,4, you are rounding down, meaning you do not change the number). The 90% confidence interval for Bernie Sanders is to

Answer 1

Answer:

The 90% confidence interval for the support of Sanders by millenials is between 53% and 57%.

$0.53 \leq p \leq 0.57$

Step-by-step explanation:

In this question we have to calculate a confidence interval (90% CI) on the proportion of millenials that had a favorable opinion on Sanders.

The sample size is n=1,754.

The p-hat, taken from the poll, is

$\hat{p}=0.55$

The estimated standard deviation is equal to:

$\sigma_p=\sqrt{\frac{p(1-p)}{N}}=\sqrt{\frac{0.55*0.45}{1754}}=0.012$

For a 90% CI, the z-value is z=1.645.

Then, the confidence interval is

$\hat{p}-z*\sigma_p\leq p\leq\hat{p}-z*\sigma_p\\\\0.55-1.645*0.012\leq p\leq 0.55-1.645*0.012\\\\0.55-0.02 \leq p \leq 0.55+0.02\\\\0.53 \leq p \leq 0.57$