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 = 0.298
Upper bound = 0.822

n = 1200

a. The point estimate of the population proportion is _____.
b. The margin of error is _____.
c. The number of individuals in the sample with the specified characteristic is _____.

Answer 1

The point estimate of the population proportion is 0.56, the margin of error is 0.262, and the number of individuals in the sample with the specified characteristic, x, is 672.

Step-by-step explanation:

To determine the point estimate of the population proportion, the margin of error, and the number of individuals in the sample with the specified characteristic (x), we use the information given for the confidence interval as well as the sample size.

1. The point estimate of the population proportion is the midpoint of the lower and upper bounds of the confidence interval. This is calculated as:

Point estimate = (Lower bound + Upper bound) / 2
Point estimate = (0.298 + 0.822) / 2
Point estimate = 1.12 / 2
Point estimate = 0.56

1. The margin of error is the distance from the point estimate to either bound of the confidence interval. This is calculated as:

Margin of error = Upper bound - Point estimate
Margin of error = 0.822 - 0.56
Margin of error = 0.262

1. The number of individuals in the sample with the specified characteristic is found by multiplying the point estimate by the sample size:

x = Point estimate × n
x = 0.56 × 1200
x = 672

Answer 2

a. 0.56

b. 0.262

c. 672

Step-by-step explanation:

Confidence interval:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the result of the subtraction between these two bounds divided by 2.

a. The point estimate of the population proportion is

Mean of the bounds. So

(0.298 + 0.822)/2 = 0.56

b. The margin of error is

(0.822-0.298)/2 = 0.262

c. The number of individuals in the sample with the specified characteristic is

0.56 of 1200. So

0.56*1200 = 672