Answer:
The point estimate = 0.507
Margin error of a given confidence interval = 0.032
Step-by-step explanation:
The point estimate is calculated by using the sample statistics of a population.
Thus; point estimate can be expressed with the formula:
[tex]\overline x = \dfrac{\sum \limits ^n _{i=1} \ x _i}{n}[/tex]
Given that : 0.475 < p < 0.539
[tex]\overline x = \dfrac{0.475+0.539}{2}[/tex]
[tex]\overline x = \dfrac{1.014}{2}[/tex]
[tex]\overline x = 0.507[/tex]
The point estimate = 0.507
The margin of error which shows the percentage of points that the derived results would differ from that of the given population value can be calculated with the formula:
Margin error of a given confidence interval = [tex]\mathtt{\dfrac{upper \ confidence \ limit - lower \ confidence \ limit }{2}}[/tex]
Margin error of a given confidence interval = [tex]\dfrac{0.539-0.475}{2}[/tex]
Margin error of a given confidence interval = [tex]\dfrac{0.064}{2}[/tex]
Margin error of a given confidence interval = [tex]0.032[/tex]
