A researcher is planning to carry out a sample survey in order to estimate the proportion of people in a very large population of interest who have shopped online in the previous 6 months.A simple random sample is to be selected but there is debate about whether to select an SRS of size 500 or of size 1000.With respect to the sample proportion,which statement best describes what can be expected to happen using these two different sample sizes?

A) The statistic will be more biased in the sample of size 500,but the variability of the statistic will be smaller.
B) Using the larger sample size will reduce the bias of the statistic,but the spread of the sampling distribution will be greater.
C) The statistic from either sample size will be unbiased,but the sampling distribution of the statistic from the sample of size 1000 will show greater variability.
D) The statistic from either sample size will be unbiased,but the sampling distribution of the statistic from the sample of size 1000 will show less variability.
E) The sample size has no effect on the sampling distribution of the statistic because the population size is very large.

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Javeria Malick · Accepted Answer

Final Answer : D, Explanation :  The sample proportion from either sample size will be unbiased because a simple random sample is being used. However, the sampling distribution of the statistic from the sample of size 1000 will show less variability compared to the sample of size 500. This is because as the sample size increases, the variability of the sampling distribution decreases. Therefore, selecting a larger sample size of 1000 would be a better choice to estimate the proportion of people who have shopped online in the previous 6 months in the population of interest.

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