Answer:
The 90% confidence interval for the support of Sanders by millenials is between 53% and 57%.
[tex]0.53 \leq p \leq 0.57[/tex]
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
[tex]\hat{p}=0.55[/tex]
The estimated standard deviation is equal to:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{N}}=\sqrt{\frac{0.55*0.45}{1754}}=0.012[/tex]
For a 90% CI, the z-value is z=1.645.
Then, the confidence interval is
[tex]\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[/tex]
