Which of the following statements is true?
According to the Central Limit Theorem, the mean of the sampling distribution is greater than the population mean.
According to the Central Limit Theorem, the mean of the sampling distribution is greater than the standard deviation.
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean as long as the sample size is large enough.
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the standard deviation.
From Internet:
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a bell curve) even if the original variables themselves are not normally distributed.
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean as long as the sample size is large enough.
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The correct statement is:
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean as long as the sample size is large enough.
The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the mean becomes approximately normally distributed, regardless of the shape of the population distribution. This means that the mean of the sampling distribution approaches the population mean as the sample size increases. Therefore, the statement "According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean as long as the sample size is large enough" is true.
To determine this, you need to understand the concept of the Central Limit Theorem and its implications for the mean of the sampling distribution. The Central Limit Theorem states that the sampling distribution of the mean, as the sample size increases, approaches a normal distribution with a mean equal to the population mean. It does not state that the mean of the sampling distribution is equal to the population mean for all sample sizes, but rather approaches it as the sample size gets larger.
Therefore, when considering the statements provided, the one that correctly reflects the Central Limit Theorem is: "According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean as long as the sample size is large enough."