# Relationship Between Sampling Mean and Population Mean

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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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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 testing to decide if it is true. We also need to collect the data as much as possible to reduce the potential sampling error.

In statistics, there is no theory which states sampling mean always understates the population mean. Sampling mean may overstate the population mean in some cases. Again, we still need to perform a hypothesis testing to decide if it is overstating or understating.

Second, there is no evidence to say that sampling mean always understates the population mean because of sampling variation. There may be other reasons which results in understating the population mean. The possible reasons are small sample size, inappropriate sampling method and so on.

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