Question

determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided
lower bound = 0.123, upper bound = 0.357, n = 1200
the point estimate of the population proportion is
(round to the nearest thousandth as needed.)
the margin of error is
(round to the nearest thousandth as needed)
the number of individuals in the sample with the specified characteristic is
(round to the nearest integer as needed.)

Explanation:

Step1: Calculate the point estimate of the population proportion

The point estimate of the population proportion $\hat{p}$ is the mid - point of the confidence interval. The formula is $\hat{p}=\frac{\text{Lower bound}+\text{Upper bound}}{2}$.
Substitute the given values: $\hat{p}=\frac{0.123 + 0.357}{2}=\frac{0.48}{2}=0.240$.

Step2: Calculate the margin of error

The margin of error $E$ is given by the formula $E=\frac{\text{Upper bound}-\text{Lower bound}}{2}$.
Substitute the values: $E=\frac{0.357-0.123}{2}=\frac{0.234}{2}=0.117$.

Step3: Calculate the number of individuals in the sample with the specified characteristic

We know that $\hat{p}=\frac{x}{n}$, so $x = n\times\hat{p}$.
Substitute $n = 1200$ and $\hat{p}=0.240$: $x=1200\times0.240 = 288$.

Answer:

The point estimate of the population proportion is $0.240$.
The margin of error is $0.117$.
The number of individuals in the sample with the specified characteristic is $288$.