It sounds from the first-generation results like smooth is dominant over wrinkled -- they all came out smooth. If you crossed first-generation hybrids with themselves, each of the hybrids would contribute one smooth and one wrinkled gene, and the table would come out like the one below.

```                           s  w
--------
s | s  s
w | s  w
```
This theory would predict 75% smooth and 25% wrinkled among the cross of two first-generation hybrids -- 3 s for every 1 w. Mendel did it 7324 times and got 5474/7324 = 74.7% smooth and 1850/7324 = 25.3% wrinkled -- pretty close!!!. In fact, too close for comfort?

The model that helps to answer this question is the following: from the infinite population of all possible 1st generation hybrid crossings Mendel took an iid sample of n=7324 1st generation hybrid crossings. You can do this problem either with sums, which keep track of the number of smooth and wrinkled plants, or with averages, which keep track of the percentages of s and w; the model I have used is based on percentages. Under Mendel's model the expected percentage of smooths is 75%, with a standard error of 0.75*0.25/7324 = .051 or 0.51%, and the observed percentage is 74.7%. This works out to a z-score of (74.7% - 75%)/0.51% = -.51. We are interested in the chance of agreement this close or closer, so we want the area in the middle between -.51 and +.51, which is about 38%. This one experiment does not indict Mendel or anybody working for him; the problem for Mendel was that every single experiment he did had agreement this good or even better, and across many experiments after awhile that starts to seem less and less plausible.

Current thinking is that Mendel's theory is right but that his data were massaged by somebody (Fisher thought it was Mendel's gardening assistant) to improve the agreement with the theory.