Question

Local community leaders are concerned about the distribution of homicides in their small town. The local police department broke the city into six recognizable neighborhoods of the same size and discovered the following distribution of homicides:

Neighborhood Number of Homicides
A 14
B 9
C 17
D 3
E 7
F 10
Community leaders would like to know whether the homicides are
randomly distributed across these six neighborhoods.
a. Use a 5% level of significance and outline each of the steps re-
quired in a test of statistical significance.
b. What can you conclude about the distribution of homicides across
these six neighborhoods?

Answer 1

To determine if homicides are randomly distributed across neighborhoods, a chi-square test of independence can be used at a 5% significance level. The calculated chi-square statistic, when compared to the critical value, indicates if the distribution is indeed random or not.

Step-by-step explanation:

To assess if homicides are randomly distributed among the six neighborhoods, we can use a chi-square test of independence which helps to determine if there is a significant difference between the expected and observed frequencies of homicides in each neighborhood. The steps in a chi-square test include:

1. Setting up the hypotheses where the null hypothesis (H0) states that the homicides are equally distributed across the neighborhoods, and the alternative hypothesis (H1) states that they are not.
2. Calculating the expected frequency for each neighborhood, assuming an equal distribution of homicides across all neighborhoods.
3. Using the observed frequencies and the expected frequencies to calculate the chi-square statistic.
4. Determining the critical value from the chi-square distribution table using the degrees of freedom (df) which is the number of neighborhoods minus one, and the significance level (0.05).
5. Comparing the calculated chi-square statistic to the critical value to decide whether to reject H0.

If the chi-square statistic is higher than the critical value, we reject H0 and conclude that the homicides are not randomly distributed among the neighborhoods. Otherwise, we do not have sufficient evidence to reject H0 and conclude that there is no significant difference in the distribution of homicides across the neighborhoods.