Sample Characteristics
Sample Size and Statistical theory - Sample Characteristics
The problem is that the population mean is not known but must be estimated from a sample. Assume that a simple random sample of size 10 is taken from the population. The 10 people selected and their respective attitudes are shown in Figure 12-2.
10
X = -jrrlXt = 0.5
iu i=l
s2 = -A_2(Xt-X)2 = ^=1.61 s = Vs2" = 1.27
Just as the population has a set of characteristics, each sample also has a set of characteristics. One sample characteristic is the sample average or mean:
n
X=-EXi = 0.5
Two means now have been introduced, and it is important to keep them separate. One is the population mean (p.), a population characteristic. The second is the sample mean (X), a sample characteristic. Because the X is a
sample characteristic, it would change if a new sample were obtained. The sample mean (X) is used to estimate the unknown population mean (p
Another sample characteristic or statistic is the sample variance (s2). which can be used to estimate the population variance (a2). Under simple random sampling, the sample variance is
n
s2 = sample variance = ——p 2 (Xx ~ X)2 = 1.61
Note that s2 will be small if the sample responses are similar and large if they are spread out. The corresponding sample standard deviation is simply2
s = sample standard deviation = Vs2 = 1.27
Again, it is important to make a distinction between the population variance (a2) and the sample variance (s2).
The problem is that the population mean is not known but must be estimated from a sample. Assume that a simple random sample of size 10 is taken from the population. The 10 people selected and their respective attitudes are shown in Figure 12-2.
10
X = -jrrlXt = 0.5
iu i=l
s2 = -A_2(Xt-X)2 = ^=1.61 s = Vs2" = 1.27
Just as the population has a set of characteristics, each sample also has a set of characteristics. One sample characteristic is the sample average or mean:
n
X=-EXi = 0.5
Two means now have been introduced, and it is important to keep them separate. One is the population mean (p.), a population characteristic. The second is the sample mean (X), a sample characteristic. Because the X is a
sample characteristic, it would change if a new sample were obtained. The sample mean (X) is used to estimate the unknown population mean (p
Another sample characteristic or statistic is the sample variance (s2). which can be used to estimate the population variance (a2). Under simple random sampling, the sample variance is
n
s2 = sample variance = ——p 2 (Xx ~ X)2 = 1.61
Note that s2 will be small if the sample responses are similar and large if they are spread out. The corresponding sample standard deviation is simply2
s = sample standard deviation = Vs2 = 1.27
Again, it is important to make a distinction between the population variance (a2) and the sample variance (s2).
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