Imagine that you are doing an exhaustive study on the children in all of the elementary schools in your school district. You are particularly interested in how much time children spend doing active play on weekends.
You find that for this population of 2,431 children, the average number of minutes spent doing active play on weekends is μ = 87.85, with a standard deviation of σ = 118.1.
You select a random sample of 25 children of elementary school age in this same school district. In this sample, you find that the average number of minutes the children spend doing active play on weekends is M = 79.07, with a standard deviation of s = 129.91.
The difference between M and μ is due to the __________.
Suppose you compile all possible samples of 25 children of elementary school age in your school district. If you calculate the mean of each sample (M) and create a frequency distribution of these means, this distribution is referred to as the __________.
The mean of this distribution, that is, the mean of all the sample means (when n = 25), is the expected value of M and will be equal to __________. The standard deviation of this distribution is called the standard error of M and will be equal to __________.
Suppose you compile all possible samples of 100 children of elementary school age in your school district; the expected value of M (when n = 100) will be __________ the expected value of M for all of the possible samples of 25 children of elementary school age in your school district. The standard error of M for this distribution of samples when n = 100 will be equal to __________.
The standard error of M for all the possible samples of 100 is __________ the standard error of M for all of the