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 equals=0.1070.107​,

upper

bound equals=0.4640.464​,

n equals=17401740

The point estimate of the population proportion is

nothing.

​(Round to the nearest thousandth as​ needed.)

The margin of error is

nothing.

​(Round to the nearest thousandth as​ needed.)

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

nothing.

​(Round to the nearest integer as​ needed.)

Answer 1

Solution :

Given that,

Lower confidence interval = 0.107

Upper confidence interval = 0.464

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

= (0.107 + 0.464) / 2

= 0.571 / 2

= 0.2855 = 0.286

The point estimate of the population proportion is = 0.286

Margin of error = E = Upper confidence interval - = 0.464 - 0.286 = 0.178

The margin of error is = 0.178

n = 1740

The number of individuals in the sample with the specified characteristic is ,

= x / n

x = * n = 0.2855 * 1740 = 496.77 = 497

The number of individuals = 497