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 boundequals0.645​, upper boundequals0.915​, nequals1500

Answer 1

The point estimate of the population​ proportion is 0.78.

The margin of error of the interval is of 0.135 = 13.5%.

The number of individuals in the sample with the specified​ characteristic is 1170.

Explanation:

Confidence interval concepts:

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 subtraction of these two bounds divided by 2.

In this question:

Lower bound: 0.645

Upper bound: 0.915

Point estimate of the population​ proportion

`p = (0.645 + 0.915)/(2) = 0.78`

The point estimate of the population​ proportion is 0.78

Margin of error for the following confidence​ interval

`M = (0.915 - 0.645)/(2) = 0.135`

The margin of error of the interval is of 0.135 = 13.5%.

The number of individuals in the sample with the specified​ characteristic

78% of 1500

0.78*1500 = 1170

The number of individuals in the sample with the specified​ characteristic is 1170.