Question

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 appearances. Let rho denote the proportion of all women who think media has a negative impact on women's health because they set unattainable standards for appearance. Find a point estimate for rho and also construct a 95% confidence interval for

Answer 1

point estimate=p=0.77

95 % confidence interval= [0.732,0.808]

Explanation:

Let p be the point estimate of rho. The point estimate can be computed as

p=x/n

p=365/474

p=0.77.

The 95% confidence interval for rho can be computed as

`p-z_{(\alpha)/(2) } \sqrt{(pq)/(n) }<rho<p+z_{(\alpha)/(2) } \sqrt{(pq)/(n) }`

where,

p=0.77

q=1-p=1-0.77=0.23

`z_{(\alpha)/(2) } =z_{(\0.05)/(2) } =z_(0.025 ) =1.96`

`0.77-1.96 \sqrt{(0.77(0.23))/(474) }<rho<0.77+1.96 \sqrt{(0.77(0.23))/(474) }`

`0.77-1.96(0.0193)<rho<0.77+1.96(0.0193)`

`0.77-0.0378<rho<0.77+0.0378`

`0.732<rho<0.808` (rounded to three decimal places).