A study of crime rates was recently taken in three cities in the United States. Neighborhoods of size 1000 were randomly sampled from three different cities (populations): New York, LA, and Washington. The number of crimes occurred in the last five years in each neighborhood were recorded. The average annual income in each neighborhood was also recorded as an index of financial well-being. (The data is in the file attached)
a) Are there differences in the mean number of crimes among the cities?
b) Are there differences in the mean annual income among the cities?
c) In first part of the question, what was the power of each test to reject the null hypothesis?
d) What were the smallest sample sizes that would have allowed you to reject the null hypothesis?
e) For the combined sample (assuming no difference among cities in mean of variance for each variable) test whether or not crime rate an income of these cities combined are representative of North American cities.
The average North American crime rate for the neighborhoods of 1000 is 10 over the course of five years. The average annual income is $1000.
**The distributions for the New York and LA data sets are normal. Washington isn't**
ANOVA has been used to test the hypotheses that there are differences in the mean number of crimes among the cities and differences in the mean annual income among the cities.