The National Assessment of Educational Progress ( NAEP) includes a mathematics test for eigth-grade students. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to an SRS of 1100 8th-graders from a large population in which the scores have mean 280 and standard deviation 129 . The mean x¯¯¯ will vary if you take repeated samples.
The sampling distribution of x¯¯¯ is approximately Normal. It has mean 280 .
What is its standard deviation
To calculate the standard deviation of the sampling distribution of the mean (x̄), we can use the formula:
Standard deviation of x̄ = (Standard deviation of population) / √(sample size)
In this case, the standard deviation of the population is given as 129 and the sample size is 1100. Plugging these values into the formula, we get:
Standard deviation of x̄ = 129 / √(1100)
To compute this value, we divide the standard deviation of the population (129) by the square root of the sample size (√1100). Let's calculate it:
Standard deviation of x̄ = 129 / √(1100)
= 129 / (√1100)
≈ 3.88
Therefore, the standard deviation of the sampling distribution of the mean (x̄) is approximately 3.88.