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Extracurricular activities and grades North Carolina State University studied student performance in a course required by its chemical engineering major. One question of interest was the relationship between time spent in extracurricular activities and whether a student earned a C or better in the course. Here are the data for the 119 students who answered a question about extracurricular activities:26(a) Calculate percents and draw a bar graph that describes the nature of the relationship between time spent on extracurricular activities and performance in the course. Give a brief summary in words.(b) Explain why you should not perform a chi-square test in this setting.

a. See histogramb. Expected values not all at least 5.

Intro Stats / AP Statistics

Chapter 11

Inference for Distributions of Categorical Data

Section 2

Inference for Relationships

Confidence Intervals

The Chi-Square Distribution

University of North Carolina at Chapel Hill

University of St. Thomas

Boston College

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Alright. The problem asked us to take the data, given the table and right as percentages and then graph and interpreted. So I went ahead and already wrote the data in the table as, uh, proportions. Because just with a calculator doesn't. It's something that you could do yourself in a matter of a minute or two. So I just took the items and divided them by the column total to get this new table, which is the proportions. And and, um, now we need to graph and interpret this. So let's draw bar graph. All right, this is my looks like my percents, co two at most 63. So we don't need to go beyond that. 10 20 30 40 50 60 a little higher to 63. So I guess I could do to 70. All right. And then we have no, no. I crammed this so far over. We definitely have enough space. Let me skewed it over a bit. That over? Okay, here we go. Categories we're going to have We have what they got as a grade, and then what? The amount of extra curricular hours that they're in. And now let's just go through. So in the first category, we have less than two hours of extra activities. And then we have, um a C or better. And then we have a D or F. McCall. Doff, dear f So see your better. We got a 55 and then for dear Africa, 45. All right, then let's do the same thing next category, which would be 2 to 12. And we have. So you're better do your If so, you're better in this category of 75 0 I guess we got higher than I thought. Thankfully, a graph is gonna fit, though, So that's way up here. And to your f is a 25 the last category, which is more than 12. And then we have. So you're better do your f sear better is gonna be a 38. Do your f is gonna be a 63. All right, third table. So for in the mess percentages up here. And then here's my graph, and I need to interpret it So we look at a graph. It appears that those who are moderately involved in extracurricular activities to 12 um, get the highest grades because they have the lowest amount of failings knows how this is pretty low. So I would say, But students in 2 12 hours, uh, extra curricular activities. I have the highest grades, all right. And it seems actually an interesting note to is it seems like having having more than 12 seems to have the most negative impact I look over here on this one. So it's kind of interesting because this one is the highest, all right? And now part B, why not use a kind squared? OK, well, there's two things to think about kind squared, where they were going to a chi squared when you do. Could some conditions. Well, first off, we have random. We have no idea how the data was gathered, so we have no idea if it was random or not. So that's that's out of the out right away. And that's pretty frankly good enough to, um, reject. This is a bad experience for Chi squared, but we could also do one other thing, and that's is let's just say we did expected counts. Well, we do expect it counts. Oh, and I raised my original data so I don't have the original numbers do, giving one second here number 40. Okay, so let's say let's do expect a council quicker. But you expect accounts, then I'm gonna have so we have C or better D or F. They have less than two 2 to 12 greater than 12 and we have. You have 100 and 19 students. 119 is my end value and my column totals my column totals and do like this. This column will have total of 20. This column had a total of 88 91. This column had a total of eight, and this row had a total of 3 37 in this row had a total of 71 81 82 82. So what do a couple expected? Council. Quick. All right, so 37 times eight divided by 119 is 2.5. So they expect account for this one is 2.5 in that right there. That is less than five. So we fail the large numbers test as well, and I'm going about doing that's the table because right off the bat, we see that this one here that messes it up even if they're the ones work. The fact that this one here is going less than five is a problem. So it's actually two reasons that we can't do a chi squared. There's the failing large numbers test and that it's not random.

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