8. Random samples of size n are drawn from a population. The mean of each sample is calculated, and the standard deviation of this set of sample means is found. Then the procedure is repeated, this time with samples of size 4n. How does the standard deviation of the second group compare with the standard deviation of the first group? A. It will be the same. B. It will be twice as large. C. It will be four times as large. D. It will be half as large. E. It will be one-quarter as large.
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Step 1: Calculate the standard deviation of the second group using the formula for sample standard deviation: \( \frac{\sigma}{\sqrt{n}} \) Show more…
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Random samples of size n are drawn from a population. The mean of each sample is calculated, and the standard deviation of this set of sample means is found. Then the procedure is repeated, this time with samples of size 4n. How does the standard deviation of the second group compare with the standard deviation of the first group? A. It will be the same. B. It will be twice as large. C. It will be four times as large. D. It will be half as large. E. It will be one-quarter as large.
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