Questions: 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 = 0.337, upper bound = 0.833, n=1000 The point estimate of the population proportion is (Round to the nearest thousandth as needed.)

Solution Steps

The point estimate of the population proportion is calculated as the midpoint of the confidence interval. Given the lower bound \( L = 0.337 \) and the upper bound \( U = 0.833 \), the point estimate \( \hat{p} \) is given by:

\[ \hat{p} = \frac{L + U}{2} = \frac{0.337 + 0.833}{2} = 0.585 \]

The margin of error \( E \) is half the width of the confidence interval. It can be calculated as:

\[ E = \frac{U - L}{2} = \frac{0.833 - 0.337}{2} = 0.248 \]

To find the number of individuals in the sample with the specified characteristic \( x \), we multiply the point estimate \( \hat{p} \) by the sample size \( n = 1000 \):

\[ x = \hat{p} \times n = 0.585 \times 1000 = 585 \]

Final Answer