According to the Central Limit Theorem, as the sample size increases, the standard deviation of the sampling distribution of the sample means will:a.Increaseb.Decreasec.Remain the samed.Cannot be detremined
Question
According to the Central Limit Theorem, as the sample size increases, the standard deviation of the sampling distribution of the sample means will:a.Increaseb.Decreasec.Remain the samed.Cannot be detremined
Solution
According to the Central Limit Theorem, as the sample size increases, the standard deviation of the sampling distribution of the sample means will:
b. Decrease
Here's why:
The Central Limit Theorem (CLT) states that the distribution of sample means approximates a normal distribution (also known as a "bell curve") as the sample size becomes larger, assuming that all samples are identical in size, and regardless of population distribution shape.
As the sample size increases, the standard deviation of the sample means (also known as the standard error) decreases. This is because the standard error (SE) is calculated as the standard deviation (σ) divided by the square root of the sample size (n). So, as n increases, the denominator of the SE equation gets larger and therefore SE itself gets smaller.
In other words, the larger the sample size, the closer all the sample means are to the population mean, hence less spread out (lower standard deviation).
Similar Questions
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