Imagine that you are doing an exhaustive study on the children in all of the mid
ID: 3242779 • Letter: I
Question
Imagine that you are doing an exhaustive study on the children in all of the middle schools in your school district. You are particularly interested in how much time children spend with parents on weekends. You find that for this population of 2, 431 children, the average number of minutes spent with parents on weekends is mu = 221.77, with a standard deviation of sigma = 195.57 You select random sample of 25 children of middle school age in this same school district. In this sample, you find that the average number of minutes the children spend with parents on weekends is M = 243.95, with a standard deviation of s = 215.13. The difference between M and mu is due to the sampling error central limit theorem sampling error law of large numbers population parameter Suppose you compile all possible samples of 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 distribution of sample means 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 221.77. The standard deviation of this distribution is called the standard error of M and will be equal to 215.13 Suppose you compile all possible samples of 100 children of middle school age in your school district: the expected value of M (when n = 100) will be less than the expected value of M for all of the possible samples of 25 children of middle 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 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 weekends among this population of 2, 431 children, would you actually compile all possible samples of a certain size? Yes NoExplanation / Answer
The difference between M and Mu is Sampling Error.
Given n = 100, S.E of Mean i.e SE(M) = SD / Sqrt(n) = 215.3 / sqrt(100) = 21.53
Given n = 25, S.E of Mean i.e SE(M) = SD / Sqrt(n) = 215.3 / sqrt(25) = 43.06
Therefore, SE of sample mean when n = 100 is less than SE of smaple mean when n = 25
because as n increases , SE decreases
Answer: Yes