A homozygous pea plant with round peas and yellow cotyledons was crossed to a wrinkled, green plant. The F1 was selfed and produced:

193 round, yellow
69 round, green
64 wrinkled, yellow
26 wrinkled, green
a) propose hypothesis that allows you to calculate expected values based on Mendel's laws.
b) perform a chi-square test to determine if the data agrees with your model

I just got into this genetics class and already don't know what's going on. Please help? Thank You

Sure! Understanding Mendel's laws and how to analyze genetic data can be challenging at first, but I'll do my best to explain.

a) In this case, we can use Mendel's laws to propose a hypothesis and calculate the expected values.

Mendel's laws state that for a monohybrid cross, where we are studying the inheritance of a single trait, such as pea shape or color, two alleles segregate during gamete formation and then randomly combine during fertilization.

Let's denote the allele for round peas as "R" (dominant) and for wrinkled peas as "r" (recessive), and the allele for yellow cotyledons as "Y" (dominant) and for green cotyledons as "y" (recessive).

The homozygous (RRYY) pea plant with round peas and yellow cotyledons is crossed with the wrinkled, green plant (rryy).
Their offspring, the F1 generation, will all be heterozygous (RrYy) for both traits since they inherited one allele from each parent.

When the F1 generation self-fertilizes, the possible genotypes and phenotypes of the offspring can be determined using Punnett squares:

R r
Y | RY rY
y | RY rY

So, the expected phenotypic ratios among the F2 generation can be calculated as follows:

Round, Yellow (RY--): 1/4 RRYY + 1/4 RrYY = 1/2
Round, Green (RYy-): 1/4 RrYy
Wrinkled, Yellow (rY--): 1/4 rrYY
Wrinkled, Green (rYy-): 1/4 rrYy

b) To perform a chi-square test to determine if the observed data agrees with the expected values, follow these steps:

1. Set up null and alternative hypotheses:
Ho (null hypothesis): There is no significant difference between the observed and expected values.
Ha (alternative hypothesis): There is a significant difference between the observed and expected values.

2. Calculate the expected counts based on Mendel's laws, as we discussed above.

3. Set up a table to compare the observed and expected counts:

Observed Expected (O - E) (O - E)^2 (O - E)^2 / E
Round, Yellow | 193 | ___ | ___ | ___ | ___
Round, Green | 69 | ___ | ___ | ___ | ___
Wrinkled, Yellow | 64 | ___ | ___ | ___ | ___
Wrinkled, Green | 26 | ___ | ___ | ___ | ___

Fill in the "Expected" counts with the values we calculated earlier.

4. Calculate (O - E) for each cell (subtract the observed count from the expected count) and fill in the table.

5. Square the (O - E) values for each cell and fill in the table.

6. Calculate (O - E)^2 / E for each cell by dividing the squared differences by the corresponding expected values and fill in the table.

7. Sum up the (O - E)^2 / E values for all cells. This will give you the chi-square statistic (Χ^2).

8. Determine the degrees of freedom (df) for the test. In this case, it will be 3 (number of phenotypic categories) - 1 (number of independent variables) = 2.

9. Look up the critical chi-square value in a chi-square distribution table for your chosen significance level (e.g., α = 0.05).

10. Compare the calculated chi-square value to the critical value. If the calculated chi-square value is greater than the critical value, reject the null hypothesis. If it is smaller, fail to reject the null hypothesis.

That's it! By following these steps, you will be able to propose a hypothesis and perform a chi-square test to determine if the observed data agrees with the expected values based on Mendelian inheritance.