1. Central Limit Theorem Aa Aa You\'re interested in how much time children spen
ID: 3359140 • Letter: 1
Question
1. Central Limit Theorem Aa Aa You're interested in how much time children spend in active play on weekends. Let x = the time (in minutes) spent in active play on weekends for the 2,431 children in the daycares in your school district. The distribution of x has a mean of = 65.87 and a standard deviation of = 87.08. The population mean and standard deviation are unknown to you (and everyone else). You select a random sample of 25 children of daycare age in this same school district. In this sample, you find that e average number of minutes the children spend in active play on weekends is x = 59.28, with a standard deviation of s = 95.79. Suppose you compile all possible samples of 25 children of daycare age in your school district. If you calculate the mean of each sample (R) 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), will be The standard deviation of this distribution is called the standard error of x and will be equal to Suppose you compile all possible samples of 100 children of daycare age in your school district; the mean of the sampling distribution of (when n = 100) will be the possible samples of 25 children of daycare age in your school district. The standard error of x for this distribution the mean of the sampling distribution of X for all of chExplanation / Answer
Q.1 (a) This distribution will be called as " sampling distribution of populaion mean"/
(b) The mean of this distribution is or the mean of all sample means = = 59.28
standard deviation of this distribution (standard error of the sample mean ) = s/ sqrt(n) = 95.79/sqrt(25) = 19.158
(C) Here of sample size is 100, the mean of sampling distribution will be SAME as the mean of the sampling distribution of sample means of size 25. children. But, the standard error is 1/2 times of sample size 25.
s/ sqrt(n) = 95.79/ sqrt(100) = 9.579 is half of sample size 25.
shape here is for sample size 100 is normal (bell shaped) with small deviation from mean.
shape here is for sample size 25 is normal (bell shaped) with large deviation from mean.
(4) No, we wouldn't actually compile all possible samples of certain size. It is just for inferential purpose.
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