Researchers cross a corn plant that is pure-breeding for...

Question

Researchers cross a corn plant that is pure-breeding for the dominant traits colored aleurone (C1), full kernel (Sh), and waxy endosperm (Wx) to a pure-breeding plant with the recessive traits colorless aleurone (c1), shrunken kernel (sh), and starchy (wx). The resulting F₁ plants were crossed to pure-breeding colorless, shrunken, starchy plants. Counting the kernels from about 30 ears of corn yields the following data.

Kernel Phenotype Number
Colored, shrunken, starchy 116
Colored, full, waxy 601
Colored, full, starchy 2538
Colored, shrunken, waxy 4
Colorless, shrunken, starchy 2708
Colorless, full, starchy 2
Colorless, full, waxy 113
Colorless, shrunken, waxy 626
6708

What is the order of these genes in corn?

Accepted Answer

Hi, everyone. Welcome back. Let's look at our next question. This question says the normal range of chi square values is determined by the number of degrees of freedom D F. And the level of significance alpha employed in general, a lower chi square value implies a better match between the observed and predicted values. Whereas a greater number suggests a worse fit. What does it mean when the chi square value exceeds the critical value? Well, to think this through, I'm going to post a portion of a chi square table. So I can kind of think about what all these values mean because and get a little confusing when I'm thinking about chi squared values. So I'm just going to put up this table portion here and this is just the first two rows of a chi squared table. The numbers in the table reflect chi squared values. The left side heroes is the number of degrees of freedom mentioned in the problem. And across the top we have different probability values And there's a squiggly line dividing the table vertically between probability values 0.20 and 0.05. That division point will be the level of significance chosen. So when analyzing results, you choose a level of significance of probability at which you decide, you're comfortable saying My results are significant. They're not due to sampling error or random chance or something else. And choosing this point is pretty standard um 0.05 or lower means I have a 5% or less chance that the variation in my results is due to random chance that it's not significant. So this right half of the chart on the right side of that level of significance is not colored in and it's labeled rejects the null hypothesis. So chi squared values on this side. So these greater chi squared values reject the null hypothesis, say that these variations mean something they're statistically significant Less than 5% chance that they're due just to sampling error, random chance or something like that. On the left side, these lower chi square values to the left of my level of significance, they're colored in red and that indicates that they fail to reject the null hypothesis. There is a greater chance that I'm comfortable with that those deviations could be due to chance. Now, the last thing I need to think about and maybe identify on my table to help me think through my question says, what does it mean when the chi square value exceeds the critical value? So the critical value in this case, I'm going to highlight in blue critical value and that would be that. So I've decided on my level of significance that probability that I want. But now I want the specific chi square value that I want my chi square to be greater than if I results are significant. That depends on the degrees of freedom. So let's say for instance that I have two degrees of freedom, which I calculate by saying the number of possible outcomes minus one and minus one. So let's say I've done an experiment where two degrees of freedom, I've decided on this 0.5 level significance. So my critical value then I look under 0.5 probability And across from 2° of freedom. And that gives me the Chi Square value of 5.99. So for our question were asked, what does it mean when the chi square value exceeds the critical value were on this right side of the table? We reject the null hypothesis. Well, with that in mind, let's look through our answer choices to evaluate this choice. A says the chi square value has no relationship with the fit between actual predicted data. Well, this is definitely incorrect. Um All we have to do is think about the formula for the chi squared value. Chi squared is the sum for each outcome of the on the top in parentheses observed minus expected values squared over the expected value. So Chi squared absolutely is a reflection of the deviation between your observed results and the expected results. So choice A is definitely not an answer. Choice B says the chi square value is insignificant. Well, this is not correct. The chi square value is actually what we're depending on to tell us. Do our results mean something? Are they due to just random chance? Are they due to sampling error or do they indicate a meaningfulness to that deviation from the expected value? So choice B is incorrect. Choice C says the observed data significantly differs from the expected value. And this is correct. As we see, we look at our critical value. If our chi square value is greater than this, then we're moving to even less chance that our deviation is due to random chance, we reject the null hypothesis um on this side of the table. So choice C is our correct answer. A chi square value exceeding the critical value shows that the observed data differs significantly unexpected values. And let's just look at choice D, it says the observed data fits the expected values perfectly well, that is not our correct answer because again, a larger chi squared value indicates a greater deviation from the expected values. So once again, we're looking at the lower chi square value implying a better match between observed and predicted values. Whereas a greater number suggests a worse fit. What does it mean when the chi square value exceeds the critical value? Choice? See the observed data significantly differs from the expected values that significant being a meaning of statistical significance that we have picked for our experiment. See you in the next video.

Key Concepts

Gene Linkage

Phenotypic Ratios

Recombinant Frequencies

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