Census data for a city indicate that 28.5% of the under-18 population is white,2
ID: 3251841 • Letter: C
Question
Census data for a city indicate that 28.5% of the under-18 population is white,28.3% black,33.5% Latino,8.6% Asian, and 1.1% other ethnicities. The city points out that of26794 police officers,64.8%
are white,
14.514.5%
black,
19.119.1%
Latino,
1.41.4%
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) Select the appropriate procedure. Choose the correct answer below.
A.
Chi-square goodness-of-fit test
B.
Chi-square test for independence
C.
Chi-square test for homogeneity
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.
The expected cell frequency condition is satisfied.
D.
It is reasonable to assume that the independence assumption is satisfied.
c) State the hypotheses. Choose the correct answer below.
Upper H 0H0:
The distribution of ethnicities in the police department
does not represent
is not independent of
is independent of
represents
the distribution of ethnicities of the city's youth.
Upper H Subscript Upper AHA:
The distribution of ethnicities in the police department
is not independent of
is independent of
does not represent
represents
the distribution of ethnicities of the city's youth.d) Test an appropriate hypothesis and state your results. Assume
alphaequals=0.05.
What is the test statistic? Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A.
The test statistic is
nothing .
(Round to the nearest integer as needed.)
B.
Since the assumptions are not satisfied, the test is not appropriate.
Determine the P-value. Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A.
The P-value is
nothing .
(Round to four decimal places as needed.)
B.
Since the assumptions are not satisfied, the test is not appropriate.
What is the result of the hypothesis test?
A.
Fail to reject
Upper H 0H0.
The P-value is greater than the level of significance.
B.
Reject
Upper H 0H0.
The P-value is greater than the level of significance.
C.
Reject
Upper H 0H0.
The P-value is less than the level of significance.
D.
Fail to reject
Upper H 0H0.
The P-value is less than the level of significance.
E.
Since the assumptions are not satisfied, the test is not appropriate.
e) Interpret the meaning of the results and state a conclusion. Choose the correct answer below.
A.
There is not sufficient evidence to conclude that the distribution of ethnicities in the police department is independent of the distribution of ethnicities of the city's youth.
B.
There is not sufficient evidence to conclude that the distribution of ethnicities in the police department does not represent the distribution of ethnicities of the city's youth.
C.
There is sufficient evidence to conclude that the distribution of ethnicities in the police department is independent of the distribution of ethnicities of the city's youth.
D.
There is sufficient evidence to conclude that the distribution of ethnicities in the police department does not represent the distribution of ethnicities of the city's youth.
E.
Since the assumptions are not satisfied, the test is not appropriate.
Explanation / Answer
a) Select the appropriate procedure.
Answer ; Chi-square test for independence
b) Check the assumptions. Select all that apply.
Answer : The counted data condition is satisfied. and The expected cell frequency condition is satisfied.
c) State the hypotheses.
Answer : Ho : The distribution of ethnicities in the police department is independent of the distribution of ethnicities of the city's youth.
Ha: The distribution of ethnicities in the police department is not independent of the distribution of ethnicities of the city's youth.
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