This is a useful exercise to help understand how statistical tests actually work. It can be done by hand using the instructions in Box 9.2, but you can do it very easily indeed if you have access to a statistical package. The body lengths of nine locusts are 6.2, 5.6, 5.3, 6.8, 6.9, 5.3, 6.3, 6.2 and 5.4 cm. The mean of this sample is exactly 6. Use a statistical package to run a single sample t test where the expected mean is set at 6.0. This will give no difference between the observed and expected mean.
(a) What would you expect the value of the t statistic to be? Run the analysis to check on this.
(b) Now, modify the expected value of the mean. Make it 5.90 and run the analysis again. Then make it 5.80, 5.75, 5.50 etc. What happens to the value of t as the difference between the observed and expected values increases? What happens to the probability