the-cell-in-the-table-that-contributes-the-most-to-the-chi-square-statistic-is-a-female-5050-chanc-2

Question

The cell in the table that contributes the most to the chi-square statistic is
(a) Female, 50–50 chance.
(b) Male, 50–50 chance.
(c) Female, almost certain.
(d) Male, almost certain.
(e) All the cells contribute equally to the test statistic.

Caleb Huber · Accepted Answer

all right, This one. We&#x27;re supposed to decide what value on the table contributes. Most kind. Score, statistic. Eso the table. Here&#x27;s and white. I&#x27;ve done some things force already because some of us just calculator work, you know, you have your totals. I&#x27;ve done that there for us. And then we need to find you Expect accounts, which is just your road column divided by the total population, which again is just calculator work. And I&#x27;ve done that here Force and gold already. Now we can answer this question. So if you want to know which one contributes the most, it&#x27;s one where the observed like I squared is observed minus expected squared, divided by expected. So the biggest contribution will come from that. This difference in the numerator of observed minus expected cause that contributes the most. So we just eyeball this real quick. The difference here in this row between the observing expected it is, you know, about one difference. The next row, as he wants to me to minus 50. That&#x27;s a difference of about 20 5 16 and 4 47 Well, that&#x27;s Teoh. 516 minus 447 Okay, this one is about 69 I&#x27;m just kind of looking at the female calm here because they&#x27;re kind of similar across. For example, if I do 5 12 minus four for two, that&#x27;s 70 So it&#x27;s pretty close. Um, next throw 7 35 and seven 177. Well, that&#x27;s about a 42 ish 7 10 minus 667 43 issues. So, yeah, this one&#x27;s about 42 and a look of the last row. This was pretty big. 101,000 and 74 minus 1000 and 38. Let&#x27;s over 100. This is ah, greater than 100. So clear the answer is going to be in this row the almost certain row and now we&#x27;ll be picky. And look at the two separately. So delicate. This left one 1st 11 174 Mine is one. Yeah, 1134 minus 1000 and 38. This is 136 and then if we do the other one, Ah, seven or 56 minus in under 91. That is about I just use my decimals to because I think it&#x27;s gonna be really close we gotta pick one. So one second. 756 This is a 1 35.2 difference. And the other one? If I do 11 this is 135.2 because this is the same. This implies that I probably rounded something off, so it&#x27;s just redo the last roll real quick. So reading the last row 26 to 5, I was 1930 divided by 4877 And then from that, I&#x27;m gonna subtract the observed value of 1174 That&#x27;s gonna be what I have for this one here. So, you know, my calculator real quick is equal to negative 1 35 point 1954 seven. There we go. There&#x27;s 10 decibels and I will do the same thing for the other one. That&#x27;s going to the same calculation. But the difference is the row. The column trouble change. So it&#x27;s gonna be 2 to 5 to there&#x27;s 1930 divided by 4877 minus. And then the observed is changed. 20 He had 7 56 50 six. Okay, we put that my calculator 135 I would warn nine, 54 07 I think they are the same. All right, so I guess it is. I guess that&#x27;s actually both I thought it was gonna be just the males, but looks like the air. Exactly. Um, the same one is positive, and one is negative, but that doesn&#x27;t make a difference. Because rumor that we do this computation, we square it. And since we square it on, the negative will go away over there. We divided by the expected amount. There&#x27;s a difference. As I go it something&#x27;s off here. We&#x27;re gonna square it so these numbers will be the same. But then we divide by the expected, and so it&#x27;s actually calculate These exactly. Do. I forgot about the denominator. Okay, so the statistic for this one that&#x27;s blue statistic for this 1st 1 is negative. 135 point. I was getting these the same around in the same way, so point to squared, but divided by, uh, the expected, which was 1038.8. The other one, it would be a positive 1 35.2 squared, but it&#x27;s gonna be divided by only 891.2. Since this one here has a smaller denominator, it is going to result in a larger number. So we know that this one is greater because there&#x27;s a smaller denominator. So the thing you that looks like they&#x27;re saying the thing that actually contributes the most to the chi square cystic is the last male outcome. So the almost certain male category, so the almost certain male category is our answer.

Anna Miller · Answer

question 20 with your mystery plots again. In this case, we&#x27;re expecting there to be cool, not treason. Which blood? Since there are 100 trees that mean we would expect there to be 25 trees in each location. So if you look acquired during quadrants, wondered before are expected values or 25 footage and then mammoth as part of the previous prompt. They already received account information average of the different. What else? So it&#x27;s 18 in 1 22 and 2 39 and three and 23 4 Now we just need to do the chi Square statistic, which is, um, count observed minus expected eat, squared, divided by expected. And so, um, in order to have the correct answer, we need to have these count valuables 1st 1 and then the expected variables as both the second because it was the denominator. Great. And then the only other thing that could be tricky is to make sure that you remember at the squared one of the answers does not have its cleared to make sure you have that. Therefore, the guardian&#x27;s air here city

R M · Answer

problem Number 58. Um, the answer is the sample is random and we can see that there are for you requiring We&#x27;re before me. A guy Where? Yes, Brendan, Man, winning the same killer. And hey, and then in pill. What a minute. Only three persons and could be at least five independence in the sample size. It&#x27;s live, man, 10% uh, population. All right. We then know that after years Ah, me. What is? The single is random.

Caleb Huber · Answer

the conditions for a chi squared. Tests are random, independent and expect accounts random being the observations randomly collected. So I need to like, make sure that when I&#x27;m picking people in the sample that picking a random sample where every next person is completely random and unbiased when how I picked the one prior independent the sample needs to be less than 10% of population. Um, because that means it&#x27;s with replacement where we treat with replacement. And I means that we can assume that whether or not you feel a certain way about something has no impact will not next person does. So you would be independent to the next person, then expected counts needs to always be created equal of five. If we look at the choices you have in this problem, the only one of these three conditions that appear of our options is the randomness choice. So when it asked which of these choices, uh, supported kind of artistic the one that are, um, we used a random simple It&#x27;s only the option talking about randomness where we&#x27;re talking about using random sample, this is the only option we use. Um, the other ones don&#x27;t fit anywhere with the remaining conditions

April Townson · Answer

for this question, let&#x27;s first review what a Chi Square test actually is. And sometimes you might see this written as this figure, which is the Greek letter chi squared, and what this is essentially is a test of whether a given observations was likely to occur by chance or random if it deviates from the expected value. So in the world of genetics and when studying heredity, let&#x27;s say we cross to hetero zygotes for a particular trait. And based off of this, we expect that 25% will be home was like its dominant, 50% will be header rows Argus and 25% will be processes or carry this A a trade, meaning that 25% will have a recess. It FINA type and 75% will have a dominant vino type. And let&#x27;s say we carry out this cross. So this is our expected cross based on our opponents clear. We cross these two individual organisms and we find that only 20% of their offspring our recesses or have the recess of Fino type and we want to know is this due to random chance and so because that&#x27;s going to happen any time. Think of whenever you flip a coin. Technically, there&#x27;s a 50% chance that you will lend on heads. But if you only performing a certain number of times, you might have more tales, uh, then head. But there is also a chance that our original expected hypothesis in this planet square is faulty. And perhaps this particular gene or trait, uh, functions at a either none one gene basis. Or maybe it functions under more complicated rules of heredity. And in order to test that, we would perform a kind of square test, and what we would need for that is, we would start out with our number of offspring. Let&#x27;s say this is an organism that produces a lot of offspring at once, so they have 100 offspring. We expect that 75 of them would have the dominant Fino type, and that 25 of them would have the recessive FINA type. After we carry out this cross, we find out that Onley 80 of them have this dominant feature type and only 20 of them have the recess of FINA type, and after that we would perform the chi square value calculation So this is Chi squared. This number one here is the degree of freedom, which I&#x27;ll explain a little later. Uh, and this is your first step in a sort of three step process. So you would calculate this some of the observed values minus the expected value squared over the expected values. There is a reason for this calculation. There are also other ways of calculating the chi square value. However, this is the most straightforward as it assures that you&#x27;re going to get a positive value by squaring your subtracted values. And you would just essentially plug in these values here and you would come up with the chi square value, which for this example is 1.33 which makes sense because this value would be one and this value would be 1/3 next what you would do, you would first make sure you know the degree of freedom, which is the number that&#x27;s usually represented in the sub script. Here. This is essentially for our particular example, it gets more complicated if you add more rows of expected and observed values. But it is the number of categories you have minus what so here we have two categories. The dominant being a type in the recess of FINA type. We could, if we knew the values of, say, the number of homes Vegas organism, sewer dominant, the number of hetero zygotes and the number of Hamas. I got a process of organisms. We could have three categories, but we don&#x27;t know those values. We only know the dominant and recessive fino tips. So in this example, we have two categories to minus. One is one, and what you do with that value is you look up or check a chi square critical value chart. There is one in your textbook. You could also look up Chi Square critical value chart, and you would get many different results, and they all give the same information. But some might have more precise percentage values. And what you&#x27;ll notice when you look at the chart is that on the X axis or the rose, there are your degrees of freedom. So you would find the first value, your degree of freedom one, and you would Onley look at numbers in that broke. You would find a space where those values in that row are either matching up with the chi square value you found or are between two chi square values. Because most of the time this value is going to be, it&#x27;s going to have a very specific probability of happening, which isn&#x27;t usually reflected in Chi square charts. So after you find this value or the numbers, that would be the the numbers that would bound it. Essentially, you would look at what columns those numbers air in. Usually they would be in decimal points. It would be 0.10 point 99.25 point, 05 etcetera. And you would put that as your P value. Your P value is the probability that all of this happens to the probability that your chi square value would occur given, uh, that your original hypothesis was correct and that you&#x27;re observed results happened by chance. So this is the value. This is the actual probability that the observed values and thus your chi square value happened due to chance. And in our case, we have a P value that&#x27;s between 10 and uh 25%. Which would be so let&#x27;s say it would be about 25%. Um, in that case, I obviously don&#x27;t know that off the top of my head. I&#x27;m just saying, Like for simplicity&#x27;s sake, you have a 25% chance that we got this value from random chance? No. The way that most statisticians work with these values in order to determine whether that is significant, not statistically significant or not is if a p value. So the probability that it happened randomly is less than or equal to 5%. Then that would be a sign that are expected. Values are original. Hypothesis should be rejected because the chances that the&#x27;s numbers would deviate are observed values would deviate so much. Um, with only 5% chance is much too low for a statistical probability to handle. So in our case, these values are well on the lower end, relatively. Speaking of the probability of happening by right of chance, they are still likely to occur given, um, our original hypothesis about how these fino types would be her trade by the offspring. And so we would basically go back to our original question and say, This is we don&#x27;t have enough evidence to reject this hypothesis, and so we can probably run with it for right now, until we have more evidence that states otherwise. So, essentially, to sum up for the purposes of this question. Chi square goodness of fit tests are used to test whether or not an observed value of the number of offspring with a particular trait or with a particular Gino type or Gino types. If you&#x27;re testing multiple traits, matches up with the expected uh, counts made by of Hun its where tests or by other knowledge of how these genes function and going from there. When we calculate that probability after performing the Chi Square test, figuring out the degrees of freedom and finding those values on our probability or P value chart, that will tell us the likelihood that those observed values came about from random chance. And if there is a low value that they came about from random chance, then that means we might have to return to our original hypothesis and revise it or reject it.

Caleb Huber · Answer

if this problem were supposed to state with provisional hypothesis is are no hypothesis for Akai. Score test should always begin with. There is no difference and then some problems. There&#x27;s no difference between human male teenagers that there&#x27;s a difference narrows. There are choices to see your be the difference between these two choices that B. It says that it&#x27;s between the female male teenagers in the sample and see says between the female and male teenagers and the population. If we are doing it Chi Square test, it&#x27;s to make a inferences about the population. So we definitely want to see note that B is clearly false because if I have a sample, I can look at the sample and make a history Graham and history. Graham is going to say whether or not there is no difference in the distribution of the sample, but but that&#x27;s irrelevant in terms of in terms of its on Tirol that it&#x27;s pretty relevant in terms of the entire population, though we can have hissed a gram with slight differences that in the grand scheme of the things we&#x27;re looking at, the whole population is still treated as being basically equivalent. We think of these two bars think this bar ah female in this bar male, so the option is

Problem

Software gives test statistic $\chi^{2}=69.8$ and…

Problem 56 Hard Difficulty

The cell in the table that contributes the most to the chi-square statistic is
(a) Female, 50–50 chance.
(b) Male, 50–50 chance.
(c) Female, almost certain.
(d) Male, almost certain.
(e) All the cells contribute equally to the test statistic.

Answer

(d) Male, almost certain

Related Courses

The Practice of Statistics for AP*

Related Topics

Discussion

Top Intro Stats / AP Statistics Educators

Srikar K.

Catherine R.

Boris M.

Megan C.

Intro Stats / AP Statistics Courses

Data And Variables

Data And Variables - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Daren S. Starnes, Daniel S. Yates, David S. Moore

The Practice of Statistics for AP*

Srikar K.

Catherine R.

Boris M.

Megan C.

Data And Variables

Data And Variables - Example 1

Additional Mathematics Questions

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

(d) Male, almost certain

The Practice of Statistics for AP*

Srikar K.

Catherine R.

Boris M.

Megan C.

Data And Variables

Data And Variables - Example 1

Daren S. Starnes, Daniel S. Yates, David S. MooreThe Practice of Statistics for AP*

Srikar K.

Catherine R.

Boris M.

Megan C.

Daren S. Starnes, Daniel S. Yates, David S. Moore

The Practice of Statistics for AP*