Aphenotypic ratio for a dihybrid cross is predicted to be 9: 3: 3: 1. the experimental values are: purple smooth = 75, white smooth = 28, purple wrinkled = 24, white wrinkled = 8. account for the difference between the expected and experimental values.

Two traits that we are examining are the color (purple/white) and the smoothness. 
In our sample, we have 135 individuals ( 75 +28+24+8= 135).

Since we know that expected ratio of a dihybrid cross, is 9:3:3:1 we can calculate what is the expected values of each phenotype is.

So, for the white wrinkled phenotype, we expect that there will be one-sixteenth of the whole sample ( there are 16 parts of the whole sample 9+3+3+1=16).
So, we multiply the whole sample- 135 with one-sixteenth (or 0.0625) and get 8,4375.
When you calculate the values for all phenotypes you get results shown in the attached excel table.
When you have your expected and experimental values you compare them with a chi-square test. (The test determines if the difference between the expected and experimental results is statistically significant).

The punnett square is the device used to predict genetics.