Problem

This quiz: 13 point(s) Question 2 of 13 possible This question: 1 point(s) possible Submit quiz 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 $=0.334$, upper bound $=0.736, n=1000$ The point estimate of the population proportion is $\square$. (Round to the nearest thousandth as needed.) The margin of error is $\square$. (Round to the nearest thousandth as needed.) The number of individuals in the sample with the specified characteristic is $\square$. (Round to the nearest integer as needed.)

Solution

Step 1 :Given the lower bound of the confidence interval is 0.334 and the upper bound is 0.736, and the sample size is 1000.

Step 2 :The point estimate of the population proportion is the midpoint of the confidence interval, which can be calculated as the average of the lower and upper bounds. So, \(\frac{0.334 + 0.736}{2} = 0.535\).

Step 3 :The margin of error is the difference between the point estimate and either the lower or upper bound of the confidence interval. So, \(0.736 - 0.535 = 0.201\) or \(0.535 - 0.334 = 0.201\).

Step 4 :The number of individuals in the sample with the specified characteristic can be calculated by multiplying the point estimate by the sample size. So, \(0.535 \times 1000 = 535\).

Step 5 :Final Answer: The point estimate of the population proportion is \(\boxed{0.535}\). The margin of error is \(\boxed{0.201}\). The number of individuals in the sample with the specified characteristic is \(\boxed{535}\).

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