Questions: Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=73 and σ=14; n=16

Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.

μ=73 and σ=14; n=16

Transcript text: Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. \[ \mu=73 \text { and } \sigma=14 ; n=16 \]

Solution

Solution Steps

Step 1: Given Information

We are provided with the following parameters:

Population mean (\( \mu \)) = 73
Population standard deviation (\( \sigma \)) = 14
Sample size (\( n \)) = 16

Step 2: Calculate the Standard Error

The standard deviation of the sampling distribution of sample means, also known as the standard error of the mean (SEM), is calculated using the formula:

\[ \text{Standard Error} = \frac{\sigma}{\sqrt{n}} \]

Substituting the given values:

\[ \text{Standard Error} = \frac{14}{\sqrt{16}} = \frac{14}{4} = 3.5 \]

Step 3: Round the Result

The standard error calculated is \( 3.5 \). Since the problem specifies rounding to one decimal place, we retain this value as is.