Questions: If the sample size is 36 and the population standard deviation is 12 , then the standard deviation of the sampling distribution for the mean is 2 . True False

Solution Steps

The sample size \( n = 36 \) and the population standard deviation \( \sigma = 12 \).

The standard deviation of the sampling distribution of the mean, also known as the standard error, is given by: \[ \text{Standard Error} = \frac{\sigma}{\sqrt{n}} \]

Substitute the given values into the formula: \[ \text{Standard Error} = \frac{12}{\sqrt{36}} = \frac{12}{6} = 2 \]

The calculated standard error is \( 2 \), which matches the given value. Therefore, the statement is True.

Final Answer