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Data collection and conclusions — Harder example

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- [Instructor] The table above, I put it to the left here, so that it all fits on the screen. The table above shows the results of a 2007 observational study that looked at the birthdays of the players on the amateur Canadian youth hockey championship team. Based on the results of this study, which of the following conclusions are valid? So we look at the different players, so this is player number nine, born on January 4th, 1988. Player number 16, born on January 10, 1987. So we have the birthdays of all of the different players on the team, and we need to make to see, what are these conclusions talking about? There is an association between players being on the 2007 amateur Canadian youth hockey championship team and being born between January 1 and June 30th in their year, in their year of birth. Alright, so it looks like we're gonna try to find some relationship, some association, between when you're born and your odds of being on this team. So let's see, there's no association between players being on the 2007 amateur Canadian youth hockey championship team and being born between January 1 and June 30th in their year of birth. Canadian hockey players born in 1987 are more likely to become professional hockey players than Canadian hockey players born in 1989. More players on the 2007 amateur Canadian youth hockey championship team were born in 1987 than any other year. So, let's actually, since we're talking about associations between when your birthday was, whether it's in kind of the first half of the year, or what year it is, let's actually do a little bit, everything is, they're not saying associations between January and February, they're really just talking about the first half of the year or comparing from one year or another. So actually, let me make a plot here. So, I'll do a little bit of a, let me do a little histogram right over here. So, let's see, we have people born as early as 1987 going all the way to 1989. So let's just talk about in the two halves of the year. So let's say that this is first half. So this is kind of, let's say one, 1/87 to 6/87. So this is of people born in the first half of 1987. This would be 7/87 to 12/87. That's the people born in the second half of 1987. And then you have, you have 1/88, to 6/88, first half of 88. And then you have the second half of 88. So 7/88 to 12/88. And then, I'm going off the screen here, let's just go, 'cause we do go all the way to '89. So then you have, then you have, you have 1/89, so January of 1989, through June of '89. So the first half of '89, and then the second half. 7/89 to 12, whoops. To 12, to 12/89. So let's see how many people there are at each of these. So in this first group, and I'm gonna color code it, this first group right over here. First half of 1987, first half of 1987, player number 16 is January '87. This is January '87, this is March '87, so that counts. This is before June, and this is, so let's see, we have one, two, three, four players. So that could be, let's see, one, two, three, four players. And that's the second half of 87. So let's see, out of the '87 folks, there's two folks in the second half. So one and two. Now, let's look at '88. So first half of '88, there, there, and there, and there. Yep, those are, so there's one, two, three, four people born in the first half of 1988. Let's see, second half of 1988, doesn't look like we have anybody. And then we just have one more person who's born in the first half, born in the first half of '89. So March '89. So they're born in the first half of '89. So just looking at this, in 1987, you have disproportionately more people born in the first half of the year than the second half of the year. Which wouldn't be true of the general population. The general population, I don't know the data for sure, but I'd expect that it's more evenly distributed. We see in '88, everyone that's born in 1988 was only born in the first half. And then in '89, we only have one data point, but they were born in the first half of the year. So let's look at this, let's look at these choices. There is an association between players on the 2007 amateur Canadian youth hockey championship team and being born between January 1 and June 30th in their year of birth. Yeah, it looks like, it looks like, you know, they have disproportionately many people born in the first half of the year, so I like this statement. We see that here. '87, disproportionate in the first half. '88, everyone's in the first half. '89, everyone's in the first half. There is no association between players being on the 2007 amateur Canadian youth hockey championship team and being born essentially in the first half of the year. Well, you can't pick both of these, only one of these two are gonna be true. Canadian hockey players born in 1987 are more likely to become professional hockey players than Canadian hockey players born in 1989. Well, we're not talking about professional hockey players. We're talking about the youth hockey championship team. So I really wouldn't be in a mood to make any statement about the probability of people becoming professional hockey players. You might say, okay, if you're on the youth team, you're more likely to become professional. But once again, the only reason why you had more people in '87 than in '89 is that we're looking at the championship team for a particular year. And in a particular year, of course, you're gonna have more folks in the older years than the folks who are younger. But then the championship team in two years, it's gonna have a bunch of people from '89, as these people mature. And we definitely can't say anything about, and that's just the youth championship team, we're not saying anything about professional hockey players. More players on the 2007 amateur Canadian, and actually, you know, we can, let's see, more players on the 2007 amateur Canadian youth hockey championship team were born in 1987 than any other year. Well yeah, this data is literally for the 2007 amateur Canadian youth hockey championship team, and we do indeed see that more folks were born in 1987, six folks were born in 1987, than the four in 1988 and the one in 1989. And so I think that is a fair, this right over here is a fair statement. Now, this was just for the 2007 team, and it'll change for the 2008 team and the 2009 team. And so I like one and four, and they have a choice, that is one and four.