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Is the following statement true or false? Explain. "If the sample size is increased, the standard deviation will increase because larger samples have more variability."

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Answer to a math question Is the following statement true or false? Explain. "If the sample size is increased, the standard deviation will increase because larger samples have more variability."

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Jett

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To determine if the statement is true or false, we need to understand how sample size affects standard deviation.

When the sample size increases, the standard deviation of the sample mean decreases. This is known as the Central Limit Theorem. Larger sample sizes lead to a more accurate estimate of the population mean, resulting in less variability in the sample means.

Therefore, the statement is false. When the sample size is increased, the standard deviation will not increase but rather decrease.

\textbf{Answer:} The statement is false.

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Is the following statement true or false? Explain. "If the sample size is increased, the standard deviation will increase because larger samples have more variability."

Answer to a math question Is the following statement true or false? Explain. "If the sample size is increased, the standard deviation will increase because larger samples have more variability."

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