In corn, red kernel color (R) is dominant to yellow (r) and smooth kernel texture (W) is dominant to wrinkled (w). Corn heterozygous for kernel color and kernel texture are interbred resulting in the following offspring.
330 red smooth
97 red wrinkled
101 yellow smooth
32 yellow wrinkled
Perform a Contingency Chi-Square analysis and determine if kernel color is independent of kernel texture.

a. Show your DF, chi square value, and p value
b. Do you reject or fail to reject the null hypothesis?
c. Is kernel color independent of kernel texture?

a. df =  3, chi-square = 1.7333, p value = 7.815

b. we fail to reject null hypothesis

c. it is independent of kernel texture

Explanation:

h0; there is independence

h1; no independence

9:3:3:1 this is the phenotypic ratio

9+3+3+1 = 16

330 red smooth  + 97 red wrinkled  + 101 yellow smooth  + 32 yellow wrinkled

total observed = 560

1. the degree of freedom = n-1

n =4, 4-1 = 3

to get the chi square computation

(O-E)²/E

expected value for red smooth,

9/16 x 560 = 315

chisquare = (330-315)²/315 = 0.7143

expected for red wrinkled

3/16*560 = 105

chisquare = (97-105)²/105 = 0.6095

expected for yellow smooth

3/16*560 = 105

chisquare = (101-105)²/105 = 0.1524

expected for yelow wrinkled

1/16 * 560 = 35

chisquare = (32-35)²/35 = 0.2571

total chisquare = 0.7143+0.6095+0.1524+0.2571

= 1.7333

with probability = 0.05, df = 3, the value of the chi square from x² table = 7.815

1.7333 < 7.815

so  we fail to reject the null

c. we conclude that kernel color is independent of kernel texture

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