Respuesta :
Answer:
[tex] \hat p=\frac{0.56137+0.60529}{2}= 0.58333[/tex]
The critical value for 95% of confidence is [tex]z_{\alpha/2}=1.96[/tex]
And since we know the total and the proportion is defined as:
[tex] \hat p=\frac{X}{n}[/tex]
If we solve for X (number of people who say yes) we got:
[tex] X= 0.58333* 504= 293.998 \approx 294[/tex]
And the best answer would be:
294
Step-by-step explanation:
We know that the confidence interval for the proportion is given by:
[tex] \hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
The margin of error can be calculated with this formula:
[tex] ME=\frac{0.60529- 0.56137}{2}= 0.02196[/tex]
And the estimation for the true proportion is:
[tex] \hat p=\frac{0.56137+0.60529}{2}= 0.58333[/tex]
The critical value for 95% of confidence is [tex]z_{\alpha/2}=1.96[/tex]
And since we know the total and the proportion is defined as:
[tex] \hat p=\frac{X}{n}[/tex]
If we solve for X (number of people who say yes) we got:
[tex] X= 0.58333* 504= 293.998 \approx 294[/tex]
And the best answer would be:
294
