Experimental Insight 2.1 describes data, collected by a ...

Question

Experimental Insight 2.1 describes data, collected by a genetics class like yours, on the numbers of kernels of different colors in bicolor corn. To test the hypothesis that the presence of kernels of different colors in each ear is the result of the segregation of two alleles of a single gene, the class counted 12,356 kernels and found that 9304 were yellow and 3052 were white. Use chi-square analysis to evaluate the fit between the segregation hypothesis and the class results.

Accepted Answer

Hi, everyone. Let's look at our next problem. It says If the smooth and wrinkled seated piece have the same expected values of 35 And observed values of 27 and 22 respectively, which of the following gives the correct probability range. And our answer choices are a 0.7 to 0.8 B 0.3 to 0.5, C 0.5 to 0.1 and D 0.1 to 0.1. So let's think about what we need to do to calculate, to calculate the correct probability range. And that is we need to calculate the chi squared value of our data. And from there, we can look up the probability range. So this has to do with proving or disproving the null hypothesis for the data, which is what's the likelihood that the variation we see in our data from the expected results is merely the chance versus being significant. So we have an equation for calculating chi squared, which is that chi squared equals the sum. And then on top we have oh minus E and parentheses squared over E where O is the observed value. Andy is the expected value. In addition, as well as the chi squared value, we're going to want to look for the number of degrees of freedom. So let's fill in our observed value and are expected values. Make a little chart here. The observed values for the smooth piece. Our question tells us is 27, An expected value is 35. Whereas for the wrinkled, The observed value is 22. Well, the expected values the same 35. So we'll fill out our equation recognizing that we need to some the amounts for each possible outcome. So for the smooth piece, we have 27, the observed value -35. And that squared note that it doesn't matter if there's a negative answer in the parentheses, since it'll be squared and the negative will go away once you square it. And then all that over 35. And then our other outcome that wrinkled piece observed minus expected 22 -35, all that squared over 35. So we do this math here And we'll end up with 1.83 plus four 0.83, Which will equal 6.56. So this is our chi squared value. Now, we just need to think about the degrees of freedom, degrees of freedom near the top. So I'm gonna go back up to the top here Is equal to N -1 Where N is the number of possible outcomes. In this case, we have two outcomes smooth or wrinkled. So that's 2 -1 equals one. So now we've got our degrees of freedom one And our cry squared value of 6.56. So to get the probability range, we need to look at a probability range table or a high squared table. So I'm going to just put up a little portion of the table including um what we're looking for here. This is something that either if you're on a test, it will be provided to you will be within your textbook. So I'm just going to put up a little portion so we can practice how to look that up on a chi squared table. So we have our table here at the top, there are different values of probability and then on the left, the degrees of freedom and then on the table are the different Kai Squared values. So we have our degrees of freedom is one. So we're looking at this first row here, one degree of freedom and our Chi squared value that we have calculated is 6.56. So when we look for these, we're looking for in row one where the degrees of freedom is one finding which two numbers our calculated high square value will be in between. So I see over here on the right side underneath the 0.01 probability, I've got the chi squared value of 6.64, which is a little below our number. And then underneath the probability of 0.001, I have a chi square value of 10.83. So our Christ squared value falls in between 6.64 and 10.83. And therefore that means that our probability range Is between .01 and .001. So I'm just gonna put a big circle around that, Let's pick that out there asterisk there. And you can see this probability chart has on the left side, it's shaded in, in red, white, it's not shaded on the right. So on the left side, if our probability range is 0.2 or higher, it fails to reject the null hypothesis. The cut off is that higher than 0. because 0.5 represents a only a 5% chance that the results are due only to random chance. So this, this lower side on the right rejects the null hypothesis. So that's why that different shading is there. So we'll look back at our answer choices again, our probability range between .1 and .001. So that's going to correspond a choice d which is 0. two, See you in the next video.

Key Concepts

Alleles and Segregation

Chi-Square Analysis

Hypothesis Testing

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