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Numerade Educator

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Problem 12 Medium Difficulty

Housing According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was
Hispanic: 28$\%$ Black: 24$\%$ White: 35$\%$
Asian: 12$\%$ Others: 1$\%$
The manager of a large housing complex in the city wonders whether the distribution by race of the complex’s residents is consistent with the population distribution. To find out, she records data from a random sample of 800 residents. The table below displays the sample data.4

Are these data significantly different from the city’s distribution by race? Carry out an appropriate test at the A 0.05 level to support your answer. If you find a significant result, perform a follow-up analysis.

Answer

26.063

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Video Transcript

question 12 were given a table. Have deserved ethnicities of people that live in this speech, your government complexes as well as he expected, um, pick ones you based off of the area's population. So we have to do is you take those They expected percentages and a couple of the actual expected numbers the multiplying them by the total number of individuals, which is 80. So I've done that here. So for Hispanic, you would expect 224 black 1 92 white to 80 Asian 96 other eight. Now we have to take archives. Great equation just observed minus accepted. And this numerator here squared to get rid of any possible on negative that could be caused by an expected value being larger than it observed and divide it by the expected value between to do this equation for all five different risk categories. Yes, we put our given observed value first to minus for Hispanic to 44. The cockpit is expected. And then you saw squared the, um, numerator and divided by 2 44 of the jam waiver. You do this for all four or five so are given to o to minus 1 92 which we calculated squared, divided by 1 92 Same thing for the next extra three com. And then you just add all five of those up to get a value up twenties explains you out. 32 Not perfect to quit the P value. You can use a calculator using the CDF equation where you put in 26.2 or 36 and then, um, 1000 calm before and it gives you a very significant P value, um, in which you conclude, conclude that there you can reject the null hypothesis that there is no difference between the observed and the expected.