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Answer :
Final answer:
In statistics, the mean of a sampling distribution of x is equivalent to the population mean, and the standard deviation of this distribution is the population standard deviation divided by the square root of the sample size. This makes the mean an unbiased estimator of the population mean when the sample size is large, satisfying the large counts condition for normal approximation.
Explanation:
The student is asking about concepts related to sampling distribution in statistics, and the goal is to match the term to its description focusing on mean and standard deviation of a sampling distribution of x.
The Central Limit Theorem for sample means averages states that if the sample size n is sufficiently large, the distribution of sample means will be approximately normal.
The mean of the sample means will equal the population mean, while the standard error of the mean, which is the standard deviation of the distribution of the sample means, will be the population standard deviation divided by the square root of the sample size n.
An unbiased estimator is a desirable property for an estimator, implying that its expected value is equal to the true value of the parameter being estimated. Therefore, a sampling distribution's mean is an unbiased estimator of the population mean.
The large counts condition is relevant to the Central Limit Theorem and ensures that the distribution of sample means approximates a normal distribution. This condition is met when the sample size is large enough.
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