4. Explain the differences in the sampling distributions of x for large and small samples under...

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4. Explain the differences in the sampling distributions of x for large and small samples under the following assumptions. Complete parts a and b. a. The variable of interest, x, is normally distributed. Choose the correct answer below. A. There are no differences, as both large and small samples will have normal sampling distributions. B. Large samples will have a normal sampling distribution due to the Central Limit Theorem, but small samples will not have a normal sampling distribution. C. Small samples will have a normal sampling distribution due to the Central Limit Theorem, but large samples will not have a sampling distribution. D. There are no differences, as neither large nor small samples will have normal sampling distributions. b. Nothing is known about the distribution of the variable x. Choose the correct answer below. A. Small samples will have a normal sampling distribution due to the Central Limit Theorem, but the sampling distribution of the large samples is unknown. B. There are no differences, as both large and small samples will have normal sampling distributions. C. Large samples will have a normal sampling distribution due to the Central Limit Theorem, but the sampling distribution of small samples is unknown. D. There are no differences, as the sampling distributions for both large and small samples are unknown. 4. Explain the differences in the sampling distributions of x for large and small samples under the following assumptions. Complete parts a and b. a. The variable of interest, x, is normally distributed. Choose the correct answer below. A. There are no differences, as both large and small samples will have normal sampling distributions. B. Large samples will have a normal sampling distribution due to the Central Limit Theorem, but small samples will not have a normal sampling distribution. C. Small samples will have a normal sampling distribution due to the Central Limit Theorem, but large samples will not have a sampling distribution. D. There are no differences, as neither large nor small samples will have normal sampling distributions. b. Nothing is known about the distribution of the variable x. Choose the correct answer below. A. Small samples will have a normal sampling distribution due to the Central Limit Theorem, but the sampling distribution of the large samples is unknown. B. There are no differences, as both large and small samples will have normal sampling distributions. C. Large samples will have a normal sampling distribution due to the Central Limit Theorem, but the sampling distribution of small samples is unknown. D. There are no differences, as the sampling distributions for both large and small samples are unknown.