How -19.6 and 19.6 and -25.8 and 25.8 Were Calculated

---

The experimenter is going to test the null hypothesis using the formula:

.

A z table shows that the null hypothesis is rejected at the 0.05 level if z is either less than -1.96 or greater than 1.96. By rearranging the equation for z and substituting first -1.96 and then 1.96 for z, one obtains:

and



Therefore, the null hypothesis is rejected at the 0.05 level if M is either less than -19.6 or greater than 19.6. If the 0.01 level is used then a z table shows that the null hypothesis is rejected if z is either less than -2.58 or greater than 2.58. Using 2.58 rather than 1.96 in the preceding formulas shows that the null hypothesis is rejected at the 0.01 level if M is either less than -25.8 or greater than 25.8.