When analyzing data, you may have to decide if a sample mean is different from a hypothesized population mean.

To do this, you must have measurement data, calculate the mean and standard deviation for your sample, and know something about the population.

For example:

• You hear that the average person sleeps 8 hours a day. You think college students sleep less. You ask 20 college kids how long they sleep on an average day.
  
  
• You get the data and the mean sleep time is 6.5 hours.
  
  
• Is this luck? Did you happen to pick a group of light sleepers by chance? Or do college kids really sleep less?
  
  
• What you are asking is whether college kids come from a population separate from the rest of society. "Society" supposedly is all the people who contributed to the mean of 8 hours a night that we hear about.

You might recognize this example from the Hypothesis Testing workshop when we introduced the idea of hypothesis tests. Here we are going to concentrate on the test statistic.