Given the following information about the sales prices of baseball cards from the 1960's:
They are known to possess a skewed-right distribution
The mean sale price is $5.25
The standard deviation is $2.80.
If a random sample of 100 cards from the 1960's is selected:
The distribution would be Normal
The mean would be $5.25
The standard error would be $0.28
The mean would be $5.25 and the standard error would be $0.28
From the given question, we know that:
Answering the question, if a random of 100 cards from 1960 is chosen, then it will be normal with a mean of $5.25 and a standard error of $0.28 .
since we already know standard deviation (σ) to be $2.80
Then, the formula for standard error is SD / √n
if you substitutes the values, then you have:
2.80 /√100
= 0.28.
Thus the standard error is $0.28.
To determine the mean you have to apply the central limit theorem which states that the sample distribution of a sample mean is approximate to the normal distribution with its mean and standard error.
Therefore, the mean remains $5.25
If you have a sample of size Y from a given population and let assume you can further compute some statistics like proportion, mean and standard deviation from the possible samples.
Now, the probability distribution of the computed statistics (mean, proportion, and standard deviation) is what is known as sampling distribution and its standard error is what is also known as standard deviation.
However, you can determine the variability of a sampling distribution by its standard deviation base on three major factors which include:
Therefore, the mean would be $5.25 and the standard error would be $0.28
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