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A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):30(a) Should we use a chi-square test for homogeneity or a chi-square test of association/independence in this setting? Justify your answer.(b) State appropriate hypotheses for performing the type of test you chose in part (a). Minitab output from a chi-square test is shown below.(c) Check that the conditions for carrying out the test are met.(d) Interpret the P-value in context. What conclusion would you draw?

a. Chi-square test of association/independenceb. $H_{0} :$ There is no association between the variables$H_{a} :$ There is an association between the variablesc. All conditions are satisfiedd. There is sufficient evidence that there is an association.

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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Where do young adults live…

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Which test again? For each…

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we don't five. We reject eso his problem. He had this data set. Um, it asks, and only I would write these down as we go. But I made a small it air at the end, so I'm just going to re read through why? Had already written up here. So we had this data. Let me grab something I can, like, highlight with two point out things. Make this there. You okay? So we have this data of here at this table, and you can total it. And then the lawsuit chi squared tests it as is the chi square test appropriate? Um, we're interested in finding whether or not gender and the place of living are statistically significant. And our data is easily organized to a table, so the chi square test makes sense. So that's we're gonna use the chi square test for that. You have pa theses their policies that there's no difference in the distributions of where male and female adults live. The alternative offices is that there is difference industry descriptions of where what? Where male and female adults live. They were. You check conditions. The conditions well, random is a condition, but the data came from random samples, thoughts, good independence. Uh, when I did this totaling here, we see there's 4854 total that is less than that number is less than 10% of population and adults swinging. Treat the observations is independent of each other. Expected counts need to be greater than equal to five. Here's table of the expected counts. We see that the smallest is still over 100 so we're definitely greater than five. So our conditions are met. So all conditions where this milk met for a chi square test. Then we are given the the data. They tell us that the chi square test when they calculate it is 11.13 And of the P value that goes with that data points are won 12. This is all given in the table data in your book. Well, this means What does this mean? It means the probably of finding a difference in distributions. At least as extreme as our sample is 0.8 which is point, which is less than 0.0.5 So it's pretty unlikely to find, uh, discretion as extreme as ours. So we're going to this reject the no hypothesis and conclude they're to be difference in the distribution of where people live. Um, at this with regards to gender since Because if you guys really small, it means that our sample seems like a really extreme case, and so we would assume that something is then wrong with our no hypothesis.

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