Dr. O. Sophila, a close friend of Dr. Ara B. Dopsis, reviews the  results Dr. Dopsis obtained in his experiment with iris plants described in Genetic Analysis 4.3. Dr. Sophila thinks the F₂ progeny demonstrate that a single gene with incomplete dominance has produced a 1:2:1 ratio. Dr. Dopsis insists his proposal of recessive epistasis producing a 9:4:3 ratio in the F₂ is correct. To test his proposal, Dr. Dopsis examines the F₂ data under the assumptions of the single-gene incomplete dominance model using chi-square analysis. Calculate and interpret this chi-square value. Can Dr. Dopsis reject the single-gene incomplete dominance model on the basis of this analysis? Explain why or why not.

Video transcript

Welcome back everyone. Let's look at our next problem. It says the observed and expected frequencies of blood types A B A B and O and A sample of 500 people are given as follows. The observed frequencies for blood groups, A B A B and O are 151 152 100 respectively. The expected frequencies for blood groups A B A B and O are 181 140 30 and respectively. What is the chi square value? And her answer choices are a 10.0 B 20. C 30.4 and D 46.42. So we'll start by looking at our formula for chi square value. I'll just paste that up here and that is K squared equals the sum of and then we have in parentheses, O minus E meaning observed value minus expected value and that value, parentheses squared divided by the expected value. So we're given our observed and expected values for each of the blood types and we need the sum of that factor for each blood type. So let's fill out our formula here. So we have K squared equals so we'll start with blood type A and we have the observed value of 150 minus the expected value, which for type A was a 180 we put that in parentheses and that is squared then divided by the expected value which was 180. Now, we will add to that the observed unexpected values according to that chi square formula for blood type B. So for blood type B, we have in parentheses, our observed value of 100 minus the expected value of 140. That difference in parentheses squared divided by the expected value of 140. Now we'll add to that, we have our A B blood group in parentheses are observed value of 50 minus our expected value of 30. That difference in parentheses squared divided by our expected value of 30. And finally, we add to that or blood type O in parentheses, I observed value of 200 minus our expected value of 150. That difference in parentheses squared divided by the expected value of 150. So we have four expressions added together. So we'll say in our next line that the K squared value equals and let's evaluate our expression for blood type A and that will give us five and then plus sign, our expression for B calculates out two, 11.43 plus sign. And then our ex expression for blood type A B which calculates out to 13.33 plus sign. Then we evaluate that expression for blood type O and we get 16 0.67. So add all those together and we get the final value of 46.43. So we'll go look at our answer choices here and we see that choice D is the closest at 46.42. Those thoughts off by 1 1/100. And that's most likely due to just differences in how I rounded the four different expressions versus how in the problem they were rounded. So we can say that the chi square value given the observed and expected frequencies of blood types A B A B and O in this sample is choice D 46.42. See you in the next video.