Question

You produced 639 plants with the following phenotypes round yellow gray 269 round yellow white 98 round green, gray 86 wrinkled yellow gray 88 round green white 27 wrinkled yellow white 34 wrinkled green gray 30 wrinkled green white 7 The (observed-expected)2 was as follows round yellow white 65.61 round green gray 15.21 wrinkled yellow gray 3.61 round green white 8.41 wrinkled yellow white 16.81 wrinkled green gray 0.01 wrinkled green white 9.00 What is the chi-square value

Answer 1

Note about the question:

Among the (observed-expected)² list, there is one value missing. This value corresponds to round yellow gray plants, and equals 0.002. This number was included in the explanation of the problem.

Answer:

The chi-square value is X² = 2.6813.

Explanation:

Available information:

Observed individuals numbers:

• Total number in the population: 639
• Round yellow gray 269
• round yellow-white 98
• round green, gray 86
• wrinkled yellow gray 88
• round green white 27
• wrinkled yellow white 34
• wrinkled green gray 30
• wrinkled green white 7

The expected numbers

• ratio 27:9:9:9:3:3:3:1
• round yellow gray 269.58
• round yellow white 89.86
• round green gray 89.86
• wrinkled yellow gray 89.86
• round green white 29.95
• wrinkled yellow white 29.95
• wrinkled green gray 29.95
• wrinkled green white 9.98

The (observed-expected) ² numbers

• round yellow gray 0.002
• round yellow white 65.61  
• round green gray 15.2
• wrinkled yellow gray 3.61
• round green white 8.41
• wrinkled yellow white 16.81  
• wrinkled green gray 0.01  
• wrinkled green white 9.00      

To get the chi-square value, we just need to replace the terms in the following equation.

                       Chi square= ∑ ((O-E)²/E)

Where,  

• ∑ is the sum of the terms

• O refers to the Observed number of individual

• E refers to the Expected numbers of  individuals

X² = ∑ ((O-E)²/E)  

X² = (0.002/269.58) + (65.61/89.86) + (15.2/89.86) + (3.61/89.86) + (8.41/29.95) + (16.81/29.95) + (0.01/29.95) + (9/9.98)

X² = 0.0000074 + 0.73 + 0.17 + 0.04 + 0.28 + 0.561 + 0.0003 + 0.9

X² = 2.6813