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+[[G11 Pre-AP Biology]]
+Punnet squares determines if there is a significant relationship between observed data and expected data.
+
+Example begin:
+let yellow be rep recessive allel y
+let green rep allele for Y
+
+p1: Yy x Yy
+
+gametes: Y, y x Y, y
+
+Example end.
+
+Chi square tutorial.
+Start off with two hypothesis.
+
+Null hypothesis ($H_0$):
+"There is not significant difference between observed and expected values of 75 yellow, 25 green peas. The differences are due to random chance alone."
+
+Alternative hypothesis ($H_A$):
+"There is a significant difference between the observed and expected values of 85, 25 green peas"
+
+Find the degrees of freedom and critical value.
+Degree of freedom: Number of categories/classes subtract 1.
+In the example, the 2 categories would have a degree of freedom of 1.
+
+Find the critical value. Find p=0.05 and degree of freedom.
+If the Chi Square is less than the critical value, accept the null hypothesis.
+Else accept alternative hypothesis.
+
+Chi square formula:$$\Sigma\frac{(o-e)^2}{e}$$
+![[Pasted image 20261026103929.png]]For the example, the formula results in 1.92, which is less than 3.84, thus it's failed to reject null hypothesis.
+
+An example conclusion for the example is "Fail to reject null hypothesis. The $x^2$ is smaller than the critical value of 3.841. There is not significant difference between the observed and expected values of yellow to green peas."
+
+Example begin:
+Let C represent purple.
+Let c represent corn.
+Let W represent wrinkled.
+Let w represent smooth.
+
+P1: CcWw x ccww
+Gametes:
+C, c, W, w x c,c,w,w
+
+|     | CW   | Cw   | cW   | cw   |
+| --- | ---- | ---- | ---- | ---- |
+| cw  | CcWw | Ccww | ccWw | ccww |
+Genotypes:
+25% Ccww
+25% ccWw
+25% ccww
+25% CcWw
+Phenotypes:
+25% purple smooth corn.
+25% yellow wrinkled corn.
+25% yellow smooth corn.
+25% purple wrinkled corn.
+
+Hypothesis:
+null
+not null
+
+Degree of freedom is 3.
+Critical value is 7.82.
+
+Expected 200 purple smooth, 200 yellow wrinkled, 200 yellow smooth 200 purple wrinkled.
+Results are 200 purple wrinkled 200 purple smooth 190 yellow wrinkled 189 yellow smooth.
+
+| Phenotype       | Observed | Expected | $\frac{(o-e)^2}{e}$ |
+| --------------- | -------- | -------- | ------------------- |
+| purple wrinkled | 200      | 195      | 0.1282              |
+| purple smooth   | 200      | 195      | 0.1282              |
+| yellow wrinkled | 190      | 195      | 0.1282              |
+| yellow smooth   | 189      | 195      | 0.1846              |
+|                 | 779      |          | 0.5692              |
+
+0.5692 is less than the critical value of 7.82, thus null hypothesis.12
+