DOING MARKETING DURING THE TURMOIL
SAMPLES OF RESPONSE RATE
On the other hand it is also possible (and also highly, highly unlikely) that none of the 50,000 are in the sample chosen, for a response rate of 0 percent. In any sample of one-tenth the population, the observed response rate might be as low as 0 percent or as high as 50 percent. These are the extreme val ues, of course; the actual value is much more likely to be close to 5 percent. So far, the example has shown that there are many different samples that can be pulled from the population. Now, let’s flip the situation and say that we have observed 5,000 responders in the sample. What does this tell us about the entire population? Once again, it is possible that these are all the responders in the population, so the low-end estimate is 0.5 percent. On the other hand, it is possible that everyone else was as responder and we were very, very unlucky in choosing the sample. The high end would then be 90.5 percent.
That is, there is a 100 percent confidence that the actual response rate on the population is between 0.5 percent and 90.5 percent. Having a high confidence is good; however, the range is too broad to be useful. We are willing to settle for a lower confidence level. Often, 95 or 99 percent confidence is quite suffi cient for marketing purposes. The distribution for the response values follows something called the binomial distribution. Happily, the binomial distribution is very similar to the normal dis tribution whenever we are working with a population larger than a few hundred people. the jagged line is the binomial distribution and the smooth line is the corresponding normal distribution; they are practically identical. The challenge is to determine the corresponding normal distribution given that a sample of size 100,000 had a response rate of 5 percent. As mentioned earlier, the normal distribution has two parameters, the mean and standard deviation. The mean is the observed average (5 percent) in the sample.