Questions: A sampling distribution of sample means has a mean equal to the population mean, μ, divided by the sample size.

A sampling distribution of sample means has a mean equal to the population mean, μ, divided by the sample size.
Transcript text: A sampling distribution of sample means has a mean equal to the population mean, $\mu$, divided by the sample size.
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Solution

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Solution Steps

Step 1: Understand the statement

The statement claims that the mean of the sampling distribution of sample means is equal to the population mean, \( \mu \), divided by the sample size.

Step 2: Recall the properties of the sampling distribution of sample means

The sampling distribution of sample means has a mean equal to the population mean, \( \mu \), regardless of the sample size. This is a fundamental property of the sampling distribution of the mean.

Step 3: Evaluate the statement

The statement incorrectly suggests that the mean of the sampling distribution of sample means is \( \mu \) divided by the sample size. This is false because the mean of the sampling distribution of sample means is simply \( \mu \), not \( \mu \) divided by the sample size.

Step 4: Conclusion

The statement is False.

Final Answer

False

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