Respuesta :
Answer:
[tex]0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419[/tex]
[tex]0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481[/tex]
And the 95% confidence interval would be given (0.419;0.481). And the best option would be:
b. .419 to .481
Step-by-step explanation:
We know the following info:
[tex]n = 1000[/tex] sample size selected
[tex]X= 450[/tex] represent the number of people who favored Candidate AT
The sample proportion would be:
[tex]\hat p=\frac{450}{1000}=0.45[/tex]
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.96[/tex]
And replacing into the confidence interval formula we got:
[tex]0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419[/tex]
[tex]0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481[/tex]
And the 95% confidence interval would be given (0.419;0.481). And the best option would be:
b. .419 to .481
