Answer:
[tex]\hat p=0.645\\\\ME=0.233\\\\x=645 \ individuals[/tex]
Step-by-step explanation:
-Given the boundaries as 0.412 and 0.878
-[tex]\hat p[/tex] is the point estimate for the population proportion and is calculated as follows:
[tex]\hat p=\frac{Upper \ Bound+Lower \ Bound}{2}\\\\=\frac{0.878+0.412}{2}\\\\=0.645\\\\[/tex]
#The margin of error, ME can be calculated for the confidence intervals using the formula:
[tex]ME=\frac{Upper \ Bound-Lower \ Bound}{2}\\\\=\frac{0.878-0.412}{2}\\\\=0.233[/tex]
#The number of individuals in the sample is the product of the point estimate and population size:
[tex]\hat p=\frac{x}{n}\\\\x=\hat pn\\\\=0.645\times 1000\\\\=645[/tex]
Hence, there are 645 individuals in the sample.
