What is a market researcher?

A market researcher collects a simple random sample of n=100 customers from its population of two million ..?

• A market researcher collects a simple random sample of n=100 customers from its population of two million customers. After anayzing the sample she states that she has 95% confidence that the mean annual income of its two million customers is between $70,000 and 85,000. Explain the meaning of this statement?

• Answer:

  As you are aware whenever you compare sample data to the population as a whole there is always likely to be some degree of error (known as sample error). The smaller the sample you take the less accurate the result is likely to be. The effect of one extreme value is likely to skew a smaller sample compared to a larger one. There are certain mathematical and statistical techniques that you can apply to determine what size sample you should obtain and what exactly the sample error is likely to be. Here the market researcher has applied these techniques and she can state that the POPULATION or REAL mean of the 2 million customers is likely to be within that range of values in 95% of occasions as predicted by the sample. Obviously anything can happen when sampling and the result is likely to be ouside that range of values on 5% of occasions. Therefore she can state that she is 95% confident that the POPULATION mean based on her sample data lies within the range, $70,000 to $85,000. She can not state that with 100% confidence as a sample error can always occur, no matter what she does. However her techniques, size of sample etc that she has applied have reduced this liklihood to be in just 5% of occasions