2. Central limit theoremImagine that you are doing an exhaustive study on the children in all of the preschools in your school district. You are particularly interested in how much time children spend with parents on weekdays. You find that for this population of 2,431 children, the average number of minutes spent with parents on weekdays is μ = 223.17, with a standard deviation of σ = 148.75. You select a random sample of 25 children of preschool age in this same school district. In this sample, you find that the average number of minutes the children spend with parents on weekdays is M = 245.49, with a standard deviation of s = 163.63. The difference between M and μ is due to the . Suppose you compile all possible samples of 25 children of preschool 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 preschool 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 preschool 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 possible samples of 25. You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the . If you were interested in how much time children spend with parents on weekdays among this population of 2,431 children, would you actually compile all possible samples of a certain size? No Yes

Question

2. Central limit theoremImagine that you are doing an exhaustive study on the children in all of the preschools in your school district. You are particularly interested in how much time children spend with parents on weekdays. You find that for this population of 2,431 children, the average number of minutes spent with parents on weekdays is μ = 223.17, with a standard deviation of σ = 148.75. You select a random sample of 25 children of preschool age in this same school district. In this sample, you find that the average number of minutes the children spend with parents on weekdays is M = 245.49, with a standard deviation of s = 163.63. The difference between M and μ is due to the    . Suppose you compile all possible samples of 25 children of preschool 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 preschool 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 preschool 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 possible samples of 25. You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the    . If you were interested in how much time children spend with parents on weekdays among this population of 2,431 children, would you actually compile all possible samples of a certain size? No Yes

Accepted Answer

Given:

N = 2431μ = 223.17σ = 148.75n =25M =245.49s =163.63

Central limit theorem Imagine that you are doing an exhaustive study on the children in all of the preschools in your school district. You are particularly interested in how much time children spend with parents on weekdays.

2. Central limit theorem