What do we have this time? Well, the types off browse favored by deer are given to us in the table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 years. Because our sample size in his 320 what we have to do is we have to use a 5% level of significance, which means that our Alfa our Alfa is 0.5 okay, 5% level of significance to test the claim that the natural distribution off the brows fits the deer feeling pattern. Okay, so it's going to be our null hypothesis are null hypothesis for this question is going to be that the natural distribution, the natural distribution off browse fits the dear feeding fat. Um, okay. And what is going to be the alternative hypothesis? The alternative hypothesis will be that the natural distribution off brows does not fit the deer feeding pattern, or I can say, and the deer feeding pattern and the dear feeding Batam are not the same or similar are not similar. All right, now we know our alphas. 0105 Now we have been given a table So that is Just look at the table. Now. First we have the type of brows, the type off. Gross. All right, this is going to be the first column, or here we have sage brush, rabbit brush. We're here. We have sage brush. Then we have Excuse me. Uh, how does this building? Okay, rabbit brush, Rabbit brush. Then we have sold brush, sold brush, then we have serviceberry. Then we have serviceberry and then the other category. Okay, so now what is the plan? Composition in steady area that is also given to US land composition in study area in study area. Now, this is also given to us. This is 32% 32%. Then this is 30 8.7%. Then this is 12%. Then this is 9.3% and then it is 8%. Okay, now the observed number of deer feeding on this plant. Which means let me just write this as the observed value, the observed values What are we observed? Values that we have? It is 102 Then it is 1 25. Then it is 43 27 in 23. Now What exactly is the sum of all of this? We need this because that is going to be our sample size. And this is 3 20. Okay, so this is our sample size. The next thing that we do in order to calculate the Chi Square statistic is to find the expected values, the expected values, the expected values for all the categories. And they're given by the sample size, the sample size, which happens to be 3. 20 in this case which is also been ordered by in multiplied by the probability the probability off each category off each category Okay, the probability or the proportion off his category that is given to us. So let us see how this is calculated. We're here. We're going to have the expected value, the expect dead values. All right, now to the calculator, I go. I use my calculator to find all the respected values. Now, for the first category is going to be 32% off 3 20 against 0.32 multiplied by 3 20 which is 102.4102 point four. Then I have 38.7% or 0.387 multiplied by 3. 20. This is 1. 23.841 23.84 Then we have 12% 0.12 multiplied by 3. 20. This is 38.4, 38.4. Then we have 9.3%. 0.93 multiplied by 3. 20 it was 29.76 29.76 and then we have 8% off 3. 20 0.8 multiplied by 3. 20. So this is 25.6 25.6. These are the expected values. Now I need to find the individual chi square values. Okay, so administrate this as individual as individual chi square values. Okay, now how exactly? What? Calculate these. Okay? The formula to calculate the individual rascal values is the difference between observed minus expected whole square divided by the expected value. And once I do this for all the categories, I will sum them all up. And this is going to give me the total high square value for my problem. So let us just look at this. This is going to be the difference between observed and expected values. So in this case, it is going to be 0.4. I square this right, I am going to square this. So the 0.16 this is divided by the expected value which is 10 2.4, which is 0.15 Or let me just write this as 0.2 Similarly, over here there is a difference of 1 25 and 1 23.84 I square this square 1.16 and I divide this by 1. 23.84 This is 0.108 Or I can just write this 0.1 Okay, then there is a difference. Off 43 38.4. I square this and I divide this by 38.4, which is 0.550 point five fight. Then there is a difference off 29.76 and 27. I square this 2.76 and I divide this by the expected value off 29.76 which is 2.0 point 255 Now I can just write this as 0.26 All right, then there is a difference off 25.6 and 23 2.6. I square this and this is divided by 25.6. So this time I have 0.2640 point 264 And then what I do is I some all of these individual chi square values up. So this is going to be 0.2 plus 0.1 plus 0.55 plus 0.26 plus 0.264 This is going to be 1.86 This is 1.86 This is the value off my chi square statistic. This is the value of Mike Rice. Question District 1.86 All right now I have my guy square statistic. Now, I wish to find out the p value right for p value. I need to find the degrees of freedom that is DF and it is given by the formula number off categories number off categories minus one. Now, how many number of categories do I have? Well, I have this away. A sage brush, rabbit brush, salt brush. So it's very and the other. So there are five categories. Right, So this is going to be fine. Minus one. Okay, this is five minus one. This is right. This a little properly. Okay, so this is five minus one. Okay, which is four now? In order to find the P value, you can either use the chi square table, which will give you an approximate value. Arrange off evil. You will not give you the exact value. Or you can use a statistical software like SPS s or R python or a chi square calculator. As I'm doing over here, I'm going to use an online calculator. I have my chi square statistic as 1.86 Okay, 1.86 animal You The freedom is four. My significant level is 5%. Right. So this is going to be at 50.5 and I hit. Calculate, this is gonna be a me the exact banding and a P value of 0.8964 and I can see that my P value is 0.8964 Now I can see that my P value is much greater than Alfa. What was my Alfa? My Alfa was 0.5 right? This is my Alfa, so I can see that my P value is much greater than my Alfa. And hence I will say that I same to reject my null hypothesis statement. Okay, let us go away and look at the alternative hypothesis. And in l a hypothesis Manal hypothesis waas that the natural distribution off browse fits the deer feeding patterns. So I will say that I do not have enough statistical evidence to say I will say that I do not have enough statistical evidence to say that the distribution this line is going to be an answer. That the distribution Okay, just a moment. Let's just look at what that line is. The distribution, the natural distribution of browse fits the distribution off browse fates and the deer feeding pattern and the deer feeding pattern are different. Are different are I can also say that whatever it in over here Yeah, I will say that I do not have enough statistical evidence to say that the natural distribution of rows fates that the natural distribution off off brows does not fit the deer feeling pattern. Okay, at 5% level of significance. So this is how we go about doing this question on this is my answer.