Which of the following statements are true regarding the general properties of s

Question

Which of the following statements are true regarding the general properties of sampling distributions?

The sampling distribution of a statistic often tends to be centered at the value of the population parameter estimated by the statistic.

The spread of the sampling distributions of many statistics tends to grow smaller as the sample size n increases.

As the sample size increases, sampling distributions of many statistics become more and more bell-shaped (more and more like normal distributions)

All of the above

None of the above

The sampling distribution of a statistic often tends to be centered at the value of the population parameter estimated by the statistic.

The spread of the sampling distributions of many statistics tends to grow smaller as the sample size n increases.

As the sample size increases, sampling distributions of many statistics become more and more bell-shaped (more and more like normal distributions)

All of the above

None of the above

Which of the following statements are true regarding the general properties of sampling distributions? The sampling distribution of a statistic often tends to be centered at the value of the population parameter estimated by the statistic. The spread of the sampling distributions of many statistics tends to grow smaller as the sample size n Increases O As the sample size increases, sampling distributions of many statistics become more and more bell- shaped (more and more like normal distributions) All of the above None of the above

Explanation / Answer

• In practice, one will collect sample data and, from these data, estimate parameters of the population distribution.

• Knowing the degree to which means from different samples would differ from each other and from the population mean would give you a sense of how close your particular sample mean is likely to be to the population mean.

• The standard deviation of the sampling distribution of a statistic is referred to as the standard error of that quantity.

• If all the sample means were very close to the population mean, then the standard error of the mean would be small.

• On the other hand, if the sample means varied considerably, then the standard error of the mean would be large.

Based on this answer is All of the above

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