Question

Determine the point estimate of the population proportion, the margin of error

Answer 1

Answer:

$\hat p=0.645\\\\ME=0.233\\\\x=645 \ individuals$

Step-by-step explanation:

-Given the boundaries as 0.412 and 0.878

-$\hat p$ is the point estimate for the population proportion and is calculated as follows:

$\hat p=\frac{Upper \ Bound+Lower \ Bound}{2}\\\\=\frac{0.878+0.412}{2}\\\\=0.645$

#The margin of error, ME can be calculated for the confidence intervals using the formula:

$ME=\frac{Upper \ Bound-Lower \ Bound}{2}\\\\=\frac{0.878-0.412}{2}\\\\=0.233$

#The number of individuals in the sample is the product of the point estimate and population size:

$\hat p=\frac{x}{n}\\\\x=\hat pn\\\\=0.645\times 1000\\\\=645$

Hence, there are 645 individuals in the sample.