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Numerade Educator

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Problem 9 Medium Difficulty

Doing homework A school newspaper article claims that 60$\%$ of the students at a large high school did all their assigned homework last week. Some skeptical AP Statistics students want to investigate whether this claim is true, so they choose an SRS of 100 students from the school to interview. What values of the sample proportion $\hat{p}$ would be consistent with the claim that
the population proportion of students who completed all their homework is $p=0.60 ?$ To find out, we used Fathom software to simulate choosing 250 SRSs of size $n=100$ students from a population in which $p=0.60$ The figure below is a dotplot of the sample proportion $\hat{p}$ of students who did all their homework.
(a) Is this the sampling distribution of $\hat{p} ?$ Justify your answer.
(b) Describe the distribution. Are there any obvious outliers?
(c) Suppose that 45 of the 100 students in the actual sample say that they did all their homework last week. What would you conclude about the newspaper article's claim? Explain.

Answer

(a) No.
(b) Shape: unimodal, symmetric, bell
Center: $.5575$shaped
Spread: $0.5$ and $0.712$
Outliers: $0.73$
(c) False.

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Video Transcript

have everyone This problem? It's about a newspaper article finding that were claiming that 60% of their students that their homework last week on. So in order to assimilate this, um, the weed took a simple random sample. We took many of them. And the graph that you see here, if we could draw notion curve, you can see shape. And this is about the proportion of students that said that they actually did their homework. So first things first. Ah, in part, either asking us is this the graph of the sample and distribution? And we have to say that it's not because, um, we would have to have a graph of all those samples so we could say no. Ah, because ah, not uh huh. Possible samples are included, right? You know, we have to look at the shape. So it looks, um, So we could say that he looks up, you know, moral. Which means there is only one curve. Show that out. It is you, Nim Auteuil. Okay. And we can also say that it's ah, symmetric. Um and we could actually draw to Bellary here. It's a metric abo this point right here, so it's Cem metric and it also be built ship curve, um, Bill Shit. And now we talk about the center. Well, the center will be at about point 55 0.55 seven life and then spread just means ah, from where the minimum wants to wear the maximum. So in this case, we could say that are spread would be approximate from 0.5 and your 0.712 So then it will be about mm to your 0.5 would be about right here and then is your 0.7 12 would be it about right here. Um And then now we have to talk about the outliers. So which is our points that for, like, different from all the other ones. So, for example, this would be now library here, so we say it's 0.73 approximately. That would be not where, um and then for the more In part c, they say, Hey, um, we actually found out that 45 out of ah 100 45 out of 100 students said that they actually did their homework, and then we have to say, Well, how do we feel given the information is a claim, right? Is just claim correct or not? And then we could say Now we would say that our claim is not correct. So we can conclude we conclude that the newspaper clean his boss. Thank you guys.