Question

You are an agricultural geneticist and you're interested in developing a strain of wheat that is resistant to herbivory by common pests. Resistiosa is a strain that is already resistant. Deliciosa is a strain that is susceptible. The first step in your research project is to uncover some information about the genetic architecture of the resistance alleles.

You cross Resistiosa to Deliciosa, then cross the F1 hybrids and examine resistance in the F2 generation. If resistance is controlled by a single locus with two co-dominant alleles, you would expect a 1:2:1 ratio of resistant : partially resistant : susceptible in the F2 generation.

The data are:

772 resistant, 1611 partially resistant, 737 susceptible

The question of interest is whether the F2s follow a 1:2:1 ratio, indicating the trait is governed by a single locus with two co-dominant alleles. Complete the 10 steps for this problem on your own, then answer the questions in this module.

Step 2: State the null hypothesis.

• A.

  The F2s follow a 1:2:1 ratio.

• B.

  The F2s do not follow a 1:2:1 ratio.

Step 3: State the alternative hypothesis.

• A.

  The F2s follow a 1:2:1 ratio.

• B.

  The F2s do not follow a 1:2:1 ratio.

Step 4: What is the correct level of alpha?

• A.

  We will use α/2=0.025 to define χ2CRIT.

• B.

  We will use α=0.05 to define χ2CRIT and observations of χ2OBS in the extreme right tail of the χ2 distribution will reject the null.

• C.

  We will use α=0.05 to define χ2CRIT and observations of χ2OBS in the extreme left tail of the χ2 distribution will reject the null.

Step 5: Which statistical test are you using?

• A.

  χ2 Contingency table test

• B.

  χ2 Intrinsic Goodness of Fit test

• C.

  χ2 Extrinsic Goodness of Fit test

• D.

  ANOVA

• E.

  Tukey's Honestly Significant Difference test

• F.

  Bonferroni's t-test

Step 6, part I: What is expected value (E_i) for the number of F2s that should be partially resistant?

Step 6, part II: What is the value of the test statistic? Round your answer to two decimal places.

Step 7: What is the critical value for the test statistic? Round your answer to two decimal places.

Step 8: How does the test statistic compare to the critical value?

• A.

  The test statistic is greater than the critical value, and in the critical zone.

• B.

  The test statistic is less than the critical value, and in the critical zone.

• C.

  The test statistic is greater than the critical value, and outside the critical zone.

• D.

  The test statistic is less than the critical value, and outside the critical zone.

Step 9: Based on this comparison, do you accept or reject your null hypothesis?

• A.

  Accept

• B.

  Reject

Step 10: What do you conclude from this analysis? Select all that are correct.

• A.

  The F2 phenotypes are in a 1:2:1 ratio.

• B.

  The F2 phenotypes are not in a 1:2:1 ratio.

• C.

  Resistance appears to be controlled by a single locus with co-dominant alleles.

• D.

  Resistance appears not to be controlled by a single locus with co-dominant alleles.

Answer 1

Step 2: State the null hypothesis. The F2s follow a 1:2:1 ratio.
Step 3: State the alternative hypothesis. The F2s do not follow a 1:2:1 ratio.
Step 4: What is the correct level of alpha? We will use α=0.05 to define χ2CRIT and observations of χ2OBS in the extreme right tail of the χ2 distribution will reject the null.
Step 5: Which statistical test are you using? χ2 Intrinsic Goodness of Fit test.



Step 8: How does the test statistic compare to the critical value? The test statistic is less than the critical value, and outside the critical zone.
Step 9: Based on this comparison, do you accept or reject your null hypothesis? Accept.
Step 10: What do you conclude from this analysis? Select all that are correct. The F2 phenotypes are in a 1:2:1 ratio. Resistance appears to be controlled by a single locus with co-dominant alleles.