Random samples of size 64 are taken from an infinite population whose mean is 160 and standard deviation is 32. The mean and standard error of the sample mean, respectively, are:
Question
Random samples of size 64 are taken from an infinite population whose mean is 160 and standard deviation is 32. The mean and standard error of the sample mean, respectively, are:
Solution
The mean of the sample mean (also known as the expected value of the sample mean) is equal to the population mean. So, the mean of the sample mean is 160.
The standard error of the sample mean is the standard deviation of the population divided by the square root of the sample size.
So, to calculate the standard error:
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Identify the standard deviation (σ) of the population. In this case, σ = 32.
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Identify the sample size (n). In this case, n = 64.
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Plug these values into the formula for standard error, which is σ/√n.
So, the standard error of the sample mean is 32/√64 = 32/8 = 4.
Therefore, the mean and standard error of the sample mean are 160 and 4, respectively.
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