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=0.422, upper bound = 0.858, n = 1200​

Answer 1

768

Explanation:

The point estimate of the population proportion is the midpoint of the confidence interval, which is the average of the lower and upper bounds:

Point estimate = (Lower bound + Upper bound) / 2

= (0.422 + 0.858) / 2

= 0.64

The margin of error is half the width of the confidence interval:

Margin of error = (Upper bound - Lower bound) / 2

= (0.858 - 0.422) / 2

= 0.218

To find the number of individuals in the sample with the specified characteristic x, we need to know the proportion of the sample with that characteristic. We can use the point estimate as an approximation:

x = n * point estimate

= 1200 * 0.64

= 768

Therefore, the number of individuals in the sample with the specified characteristic is 768.