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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.

(d) Male, almost certain

Intro Stats / AP Statistics

Chapter 11

Inference for Distributions of Categorical Data

Section 2

Inference for Relationships

Confidence Intervals

The Chi-Square Distribution

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all right, This one. We're supposed to decide what value on the table contributes. Most kind. Score, statistic. Eso the table. Here's and white. I've done some things force already because some of us just calculator work, you know, you have your totals. I'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'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'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's a difference of about 20 5 16 and 4 47 Well, that's Teoh. 516 minus 447 Okay, this one is about 69 I'm just kind of looking at the female calm here because they're kind of similar across. For example, if I do 5 12 minus four for two, that's 70 So it's pretty close. Um, next throw 7 35 and seven 177. Well, that's about a 42 ish 7 10 minus 667 43 issues. So, yeah, this one's about 42 and a look of the last row. This was pretty big. 101,000 and 74 minus 1000 and 38. Let'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'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'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'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'm gonna subtract the observed value of 1174 That'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's 10 decibels and I will do the same thing for the other one. That's going to the same calculation. But the difference is the row. The column trouble change. So it's gonna be 2 to 5 to there'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'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'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's a difference. As I go it something's off here. We're gonna square it so these numbers will be the same. But then we divide by the expected, and so it's actually calculate These exactly. Do. I forgot about the denominator. Okay, so the statistic for this one that'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'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's a smaller denominator. So the thing you that looks like they'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.

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