Question 1113285: A student weighed a sample of 100 industrial diamonds. She found that the sample average weight was 4.80 grams and the SD was 0.28 grams. In the context of this setting, explain what is meant by the sampling distribution of an average.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! For a large sample size (100 ≥ 30), the sample mean(4.80 grams) is approximately normally distributed, regardless of the distribution of the population the sample was taken from(this is the Central Limit Theorem).
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This means if we keep repeating this sample size with replacement, we will find that 50% of the calculated sample means will fall below 4.80 and 50% of the sample means will fall above 4.80.
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Since the population's standard deviation is unknown, we use a sample estimate to scale(standard error). The standard error of the mean is the sample standard deviation(0.28) divided by the square root of 100. The standard error and the sample mean are used in the calculation of statistical confidence intervals.
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