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.