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Relationship Between Sampling Mean and Population Mean

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Drug manufacturer knows that for a certain antibiotics, the average number of doses ordered for a patient is 20. Steve Simmons, a salesman for the company, after looking at 1 day's prescription orders for the drug in his territory, announced that the sample mean for this drug should be lower. He said, "For any sample, the mean should be lower, since the sampling mean always understates the population mean because of sampling variation." Is there any truth to what Simmons said? Explain.

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The solution gives detailed discussion on the relationship between sampling mean and population mean.

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Hi, there is no truth to what Simmons said because there is no evidence to support what he says.

First, there is no evidence to say that sampling mean always understates the population mean. We need to perform a hypothesis ...

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