The correct statement about sampling distributions is:
D. Sampling distributions get closer to normality as the sample size increases.
This is in accordance with the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution, provided the sample size is sufficiently large.
Let's briefly clarify why the other options are false:
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A. Sampling distributions are always nearly normal. (False; while larger sample sizes lead to a more normal distribution, smaller sample sizes may not yield a normal distribution, especially if the original population is not normal.)
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B. Shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is. (False; the shape of the sampling distribution changes with sample size and generally approaches normality as the sample size increases.)
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C. Sampling distribution of the mean is always right skewed since means cannot be smaller than 0. (False; this statement is incorrect because sample means can take on any value, including values less than 0, depending on the population distribution.)
Therefore, only option D is true.