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 parameter.
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 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.
D) It is a lurking variable whose value is unknown.
E) It is a statistic,but its behavior cannot be determined because only one sample is to be taken.

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Stanley Asiegbu · Accepted Answer

Final Answer : C, Explanation :  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. This is because simple random sampling ensures that each individual in the population has an equal chance of being chosen, and the sample proportion is calculated based on the number of individuals in the sample with the given characteristic. The larger the sample size, the more accurate the estimate of the population proportion will be, but the variability of the sample proportion will remain constant regardless of population size as long as the sample is small compared to the population.

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