A city is accused of having a non-diverse police force that does not fully represent the various ethnicities who reside there. Data from the most recent census are given in the table below, as well as results from a sample of 133 randomly chosen police officers. Ethnicity White African-American Latino Asian Other % of city population 41.0% 29% 18% 9.8% 2.2% Number of police officers 67 32 20 7 7 (a) Which hypotheses should be tested to determine if the ethnic make-up of the police force is consistent with the city's population? H0: , implying the police force ethnicity is (consistent/ inconsistent) with the city's population. Ha: , implying the police force ethnicity is (consistent/ inconsistent) with the city's population. (b) The residual for the African-American category is -1.058. What does the negative sign imply? There are (more/ fewer) African-American police officers than expected for this city. (c) The test statistic is 13.085. What is the p-value? (Use 4 decimals.)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A city is accused of having a non-diverse police force that does not fully represent the various ethnicities who reside there. Data from the most recent census are given in the table below, as well as results from a sample of 133 randomly chosen police officers.
| Ethnicity | White | African-American | Latino | Asian | Other |
|---|---|---|---|---|---|
| % of city population | 41.0% | 29% | 18% | 9.8% | 2.2% |
| Number of police officers | 67 | 32 | 20 | 7 | 7 |
(a) Which hypotheses should be tested to determine if the ethnic make-up of the police force is consistent with the city's population?
H0: , implying the police force ethnicity is (consistent/ inconsistent) with the city's population.
Ha: , implying the police force ethnicity is (consistent/ inconsistent) with the city's population.
(b) The residual for the African-American category is -1.058. What does the negative sign imply?
There are (more/ fewer) African-American police officers than expected for this city.
(c) The test statistic is 13.085. What is the p-value? (Use 4 decimals.)
Step by step
Solved in 4 steps with 1 images
