A sample is to be selected from a large population using simple random sampling. The proportion of subjects in the sample that have a given characteristic is to be calculated. Which of the following best describes the sample proportion?

(A) It is a lurking variable whose value is unknown.
(B) It is a statistic, which is unbiased for the population parameter only if the population is at least 100 times larger than the sample.
(C) It is a parameter.
(D) It is a statistic that is unbiased, and its variability does not depend on the population size provided the population is at least 100 times larger than the sample.
(E) It is a statistic, but its behavior cannot be determined because only one sample is to be taken.

Option D is correct.

The sample proportion is a statistic that is unbiased, and its variability does not depend on the population size provided the population is at least 100 times larger than the sample.

Step-by-step explanation:

A population proportion is the fraction of the population that possesses a particular characteristic. It is a population parameter.

A population parameter describes a characteristic (usually a numerical characteristic) for the entire population.

while

The sample proportion represents a fraction of the sample that possesses a particular characteristic. It is a statistic

A statistic describes a characteristic (usually a numerical characteristic) for the sample.

In Statistics, the sample proportion is a statistic that is always assumed to be unbiased and the variability is given as

σₓ = (σ/√n) for sample sizes less than 100

where σₓ is the standard deviation of sample means or sample proportions.

σ is the standard deviation for the population.

n = sample size

From the formula, it is evident that at lower values of n (small sample sizes) the variation in the distribution of sample means is considerable, but at large values of n; for example, values of n greater than 100, σₓ begins to reduce to zero.

σₓ = (σ/√n) as n ---> large values,

σₓ ---> 0 and the variations in the distribution of sample means becomes non-existent.

So, the sample proportion is a statistic which is unbiased and its variability does not depend on the population size provided the population is at least 100 times larger than the sample

Hope this Helps!!!

something over 10 so ? /10

step-by-step explanation: