Question

In: Biology

Two purple sea slugs are mated with each other. Among their numerous offspring, 428 have a...

Two purple sea slugs are mated with each other. Among their numerous offspring, 428 have a purple integument and 152 have orange integuments. With a chi-square test, compare the observed numbers with a 3:1 ratio and determine if the difference between observed and expected could be a result of chance.

Solutions

Expert Solution

Mendel Monohybrid cross-3:1 ratio.

Null Hypothesis: Difference between observed and expected could not be a result of chance.

Alternate Hypothesis: Difference between observed and expected frequencies could be a result of chance.

Level of Significance: 5% or 0.05.

Mendel's Monohybrid Ratio = Purple Integument : Orange Integument  - 3 : 1.

Observed Frequencies = 428 : 152 (or) 428 + 152 = 580.

Expected Frequencies = Purple Integument : Orange Integument = 435 : 145.

We can calculate expected frequencies like this,

3 / 4 * 580 = 0.75 * 580 = 435 (Purple Integument).

1/4 * 580 = 0.25 * 580 = 145 (Orange Integument).

Variables Observed (O) Expected (E) (O - E) / E
Purple Integument 428 435 - 7 49 49 / 435 = 0.11
Orange Integument 152 145 7 49 49 / 145 = 0.33
Total 580 580 = 0.44

Calculation:

= / E

O - Observed Value.

E - Expected Value.

= / E

= 0.44.

Degrees of freedom is number of classes - 1. (Class 1 - Purple Integument, Class 2 - Orange Integument)

Degrees of freedom = n - 1 = 2 - 1 = 1.

For 1 degrees of freedom, at 5% level of significance the table value is 3.84.

The calculated value of (0.44) is less than the table value (3.84)

Therefore, the null hypothesis is accepted, that is the difference between observed and expected could not be a result of chance.


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