The population mean may be 66.
Our initial hypothesis is
Since we do not claim to have knowledge either way, our alternative hypothesis is
Since we do not know the population standard deviation, although the population is normal, we must use a t-test with 9 = 10-1 degrees of freedom.
The sample mean is
The sample standard deviation is
Our test statistic is
In this case t is approximately
If we consult a t-table, we see that the value of 67.8 deviates enough from 66 for us to reject the null hypothesis if our tolerance is
If you are doing this work on a TI-83/84 calculator, the T-Test will reveal that the area of the rejection region is approximately