Chapter 26, Problem 7E

To determine

To test an appropriate hypothesis.

Answer to Problem 7E

There is sufficient evidence to reject the claim that police officers reflects the ethnic of the city’s youth.

Explanation of Solution

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:p_1=29.2\%,p_2=28.2\%,p_3=31.5\%,p_4=9.1\%,p_5=2\%,\\ H_a:Atleastoneofthe{p}_i’sdifferent\end{array}$

Observed and expected can be found as,

Compositions	Expected	Observed
White	0.292*26181	0.648*26181
Black	0.282*26181	0.145*26181
Latino	0.315*26181	0.191*26181
Asian	0.091*26181	0.14*26181
Other	0.02*26181	0

Therefore, using excel,

  

  ${\chi }^2$ = 16513.68 and P-value = 0

Decision: The p-value< 0.05, reject H0.

Conclusion: There issufficient evidence to reject the claim that police officers reflects the ethnic of the city’s youth.