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Census data for a city indicate that 29.0​% of the​ under-18 population is​ white, 26.2​% ​black,...

Census data for a city indicate that 29.0​% of the​ under-18 population is​ white, 26.2​% ​black, 33.2​% Latino, 9.5​% ​Asian, and 2.1​% other ethnicities. The city points out that of 25,577 police​ officers, 64.8​% are​ white,14.5​% ​black, 19.1​% ​Latino, 1.4​% ​Asian, and the remaining are other ethnicities. Do the police officers reflect the ethnic composition of the​ city's youth? Complete parts a through e below.

A) What is the appropriate test?

B) What is the null and alternative hypothesis?

C) What is the chi squared test statistic

D) what is the p value

Solutions

Expert Solution

Here we are provided with the census data for a city indicating the percentages of different communities of youths aswell as the respective proportions of police officers of the same communities.The total no. of police officers are also provided, 25577. We are to test wheather the police officers reflect the ethnic composition of the​ city's youth or not?

a. Here the appropriate test is the pearsonian test fror.

b. Thus the hypothesis is stated as: Ho:p1=p1*,p2=p2*,......,pk=pk* vs H1: at least on inequality in Ho

where pi s are the poppulation proportion of the ith class of the youth(unknown to us) and pi* s are the known value of the proportions(already given). and k is the total no. of class, here k=5

Now we take a random sample of size n(=25577) from the police poppulation and let fi is the sample members belonging to the ith class.

Thus the appropriate test statistics is given as:

T=  

Which under Ho follows a chi-sq distribution with (5-1) degrees of freedom and we reject our null hypothesis if the observed T is more than the upper alpha(=0.05) point of a chisq distribution with df=4

The observed T is given as: 26738.78; df=4

The upper alpha(=0.05) point of a chisq distribution with df=4 is 9.49

Thus we reject the null hypothesis and conclude based on our data that the police officers do not reflect the ethnic composition of the​ city's youth.

d. The p-value is given as: 2*min{P(T>Tobs),P(TTobs)) and it is given as 0 under Ho, in this case.

milcah answered 10 months ago
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