Respuesta :
Answer:
a. 7700, (.7321, .8079)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
Z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
In a survey of 474 U.S. women, 365 said that the media has a negative effect on women's health because they set unattainable standards for appearance. This means that [tex]n = 474, \pi = \frac{365}{474} = 0.77[/tex]. The point estimate is 0.77.
95% confidence interval
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.96\sqrt{\frac{0.77*0.23}{474}} = 0.7321[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.96\sqrt{\frac{0.77*0.23}{474}} = 0.8079[/tex]
The correct answer is:
a. 7700, (.7321, .8079)
