Census data for a city indicate that 26.2% of the under-18 populaton is white 29

Question

Census data for a city indicate that 26.2% of the under-18 populaton is white 29 7% blad, 33.6% Latino, 84% As an and 21% other ethnicities The city points out that of 26 844 police offiors, 64 8% are white 14.5% black, 19.1% Latino, 1.4% Asar, and the remaining are other ethnicites. Do the police, officers rofiect the eth c composition of the city's youth? Complete parts a through e below a) Select the appropriate procedure. Choose the correct answer below O A. Chi-square test for homogeneity O B. Chi-square test for independence O C. Chi-square goodness-of-ft test b) Check the assumptions. Select all that apply A. The counted data condition is satisfied B. It is reasonable to assume that the randomization condition is satisfied. C. It is reasonable to assume that the independence assumption is satisfied D. The expected cell frequency condition is satisfied.

Explanation / Answer

(a) we will use chi-square goodness of fit test.

(b) All four conditions are justified.

(c) In Null Hypothesis we will use " Independent of" the distribution

In Alternative Hypothesis , we will use " not independent of " the distribution.

(d) The test statistic is calculated with the help of contingecy table

here X2 = (Oi - Ei)2 /Ei

where Oi - observed table and Ei = expected table

Test Statistic X2 = 21061

(e) P - value =CHIINV (X2 > 21061, 4) = 0

Observed Expected (O-E)^2 (O-E)^2/E White 17395 7033 107366568 15265.83 black 3892 7973 16648750 2088.228 latino 5127 9020 15150622 1679.747 Asian 376 2255 3530941.6 1565.9 Others 54 564 260136.72 461.4611 Total 26844 26844 21061.17

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