There are MANY statistics we can compute and MANY ways to determine the probability in various cases.
Now, you’ve got a mean and s.d. The mean is 20. The SAMPLE (experimental) mean is 19.6. The number of subjects is 60. The s.d. is 1.40.
Now, we need to compute some test statistic using these numbers to determine if it is “likely” (probability greater or less than .05) that this mean is just random fluctuation from the population mean of 20.
The formula is
(sample mean - population mean) / s.d mean = z
The formula for the sample mean standard deviation is
s.d. / sort(n) = 1.40/sqrt (60) = 1.40 / 7.75 = .18
Now, we go back to:
(sample mean - population mean) / s.d mean = z
(19.6 - 20) /.18 = z
-.4/.18 = z
-2.22 = z
We then go to a z table and look up z = 2.22; I get .9868.
In terms of "p value", I won't comment. There are several philosophies on this. Some would say that it is whatever your alpha was when you designed the experiment. Others would claim that it is
(1 - .9868) x 2 (two tailed test).
always,
tony