According to the Census Bureau, the distribution by ethnic backgrounds of the New York City population in recent years 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 random sample of 800 residents. The table below displays the sample data:RaceHispanicBlackWhiteAsianOthersCount2122022709422Are these data significantly different from the city's distribution by race? Carry out an appropriate test at the 0.05 significance level to support your answer. C. Identify the rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical value.

Given Information: Hispanic: 28%, Black: 24%, White: 35%, Asian: 12%, Others: 1% Significance level = 0.05 State the hypothesis as follows: Null Hypothesis: H0: The distribution of race in the complex is the same as the population distribution. Alternative Hypothesis H1: The distribution of race in the complex is not the same as the population distribution.Expected counts are calculated as follows: Race Hispanic Black white Asian Others Total Count 212 202 270 94 22 800 Expected count 800×28100=224 800×24100=192 800×35100=280 800×12100=96 800×1100=8 800 Test statistic is given by the formula: χ2=∑iOi-Ei2Ei=212-2242224+202-1922192+.......22-828=26.06 Thus, the value of the test statistic is 26.06 Critical value at degrees of freedom df=n-1=5-1=4 and 0.05 significance level is 9.4877 (c) Since, computed value of the test statistic is greater than the critical value, it falls in the rejection region. So, reject the null hypothesis at 5% significance level. There is convincing evidence that the distribution of race in the complex is not the same as the population distribution

Answered: According to the Census Bureau, the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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According to the Census Bureau, the distribution by ethnic backgrounds of the New York City population in recent years 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 random sample of 800 residents. The table below displays the sample data:

Race	Hispanic	Black	White	Asian	Others
Count	212	202	270	94	22

Are these data significantly different from the city's distribution by race? Carry out an appropriate test at the 0.05 significance level to support your answer.

C. Identify the rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical value.

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