Question

Census data for a city indicate that 64.4​% of the​ under-18 population is​ white, 14.5​% black, 19.5​% Latino, 1.4% ​Asian, and 0.2​% other ethnicities. The city points out that of 25,0092 police​ officers, 64.8​% are​ white, 14.5​% ​black, 19.1​% ​Latino, and 1.4​% Asian. Do the police officers reflect the ethnic composition of the​ city's youth? Test an appropriate hypothesis and state your conclusion.​ (Assume a significance level of alphaαequals=0.05​)

A) Compute the chi-square statistic

B) Compute the P-Value

Answer 1

Ho: The police officers reflect the ethnic composition of the city's youth i.e there is no significant deviation of the observed values from expected values

Ha: The police officers do not reflect the ethnic composition of the city's youth

Let's compute the chi-square statistic using the given formula:

The calculations are shown in the following table:

	Expected %	Observed %	Oi (%*250092)	Ei (%*250092)	(Oi-Ei)^2/Ei
White	64.40%	64.80%	162059.6	161059.2	6.214
Black	14.50%	14.50%	36263.34	36263.34	0
Latino	19.50%	19.10%	47767.57	48767.94	20.520
Asian	1.40%	1.40%	3501.288	3501.288	0
Other	0.20%	0.20%	500.184	500.184	0
				Total = Chi-square Value =	26.734

Chi-square = 26.734

b) P-value at df = 5 - 1 = 4 and chi-square = 26.734 is <0.001

As the p-value < 0.001, we will reject the null hypothesis.

We conclude that there is a significant deviation between the observed and expected values. Hence, the police officers do not reflect the ethnic composition of the city's youth.