2. Central limit theorem Imagine that you are doing an exhaustive study on the children in all of the daycares in your school district. You are particularly interested in how much time children spend in active play on weekends. You find that for this population of 2,431 children, the average number of minutes spent in active play on weekends is u = 65.87, with a standard deviation of a = 87.08. You select a random sample of 25 children of daycare age in this same school district. In this sample, you find that the average number of minutes the children spend in active play on weekends is M = 59.28, with a standard deviation of s = 95.79. The difference between M and u is due to the Suppose you compile all possible samples of 25 children of daycare 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 daycare 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 daycare age in your school district. The standard error of M for this distribution of samples when n = 100 will be equal to
2. Central limit theorem Imagine that you are doing an exhaustive study on the children in all of the daycares in your school district. You are particularly interested in how much time children spend in active play on weekends. You find that for this population of 2,431 children, the average number of minutes spent in active play on weekends is u = 65.87, with a standard deviation of a = 87.08. You select a random sample of 25 children of daycare age in this same school district. In this sample, you find that the average number of minutes the children spend in active play on weekends is M = 59.28, with a standard deviation of s = 95.79. The difference between M and u is due to the Suppose you compile all possible samples of 25 children of daycare 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 daycare 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 daycare age in your school district. The standard error of M for this distribution of samples when n = 100 will be equal to
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Transcribed Image Text:2. Central limit theorem
Imagine that you are doing an exhaustive study on the children in all of the daycares in your school district. You are particularly interested in how
much time children spend in active play on weekends.
You find that for this population of 2,431 children, the average number of minutes spent in active play on weekends is u = 65.87, with a standard
deviation of o = 87.08.
You select a random sample of 25 children of daycare age in this same school district. In this sample, you find that the average number of minutes the
children spend in active play on weekends is M = 59.28, with a standard deviation ofs = 95.79.
The difference between M and u is due to the
Suppose you compile all possible samples of 25 children of daycare 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 distrib
ion is called the standard error of M and will be equal to
Suppose you compile all possible samples of 100 children of daycare 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 daycare 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 in active play on weekends among this population of 2,431 children, would you actually
compile all possible samples of a certain size?
O No
O Yes
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