Question

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.

Answer 1

Answer:

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!!!