Imagine that you are doing an exhaustive study on the children in all of the mid
ID: 2935915 • 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 doing homework on weekdays. you find that for this population of 2,431 children, the average number of minutes spent doing homework on weekdays is = 39.49, with a standard deviation of = 47.94. You select a 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 doing homework on weekdays is M- 43.44, with a standard deviation of s - 52.73. The difference between M and is due to the-sampling error Suppose you compile all possible samples of 25 children of middle 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 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 called the standard error of M and will be equal to 9.59 . 39.49 The standard deviation of this distribution is 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 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 expected value of M for all of the possible samples of 25 the standard error of M for all of the The standard error of M for all the possible samples of 100 is 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 doing homework on weekdays among this population of 2,431 children, would you actually compile all possible samples of a certain size?Explanation / Answer
the expected value of M when n = 100 will be 39.49 and SE of M of this distribution when n = 100,
SE = 49.94/sqrt(100) = 4.994
The stnadard error of M for all the possible samples of 100 is less than the SE of M for all of the possible samples of 25.
You can predict the size of SE of M for a sample size of 100 relative to a sample size of 25 beacuasue of the sqrt(n) i.e. sample size increase