In: Math
A criminologist conducted a survey to determine whether the incidence of certain types of crime varied from one district of a large city to another. The particular crimes of interest were assault, burglary, larceny, and homicide. The following table shows the number of crimes committed in four districts of the city during the past year.
Type of Crime
District |
Assault |
Burglary |
Larceny |
Homicide |
Total |
1 |
164 |
120 |
453 |
20 |
|
2 |
312 |
198 |
998 |
27 |
|
3 |
260 |
195 |
460 |
12 |
|
4 |
282 |
177 |
392 |
21 |
|
Total |
Can we conclude from the data at the 0.01 significance level that the occurrence of these types of crime is dependent on the city district?
Can we conclude from the data at the 0.01 significance level that the occurrence of these types of crime is dependent on the city district?
Note: The confidence level is equivalent to 1 – α. So, if your significance
level is 0.05, the corresponding confidence level is 95%.
Note: You can use the functions qchisq() in R to help you in solving the following.
Why we are using qchisq() function in R?
The qchisq() function in R allows us to specify a desired area in a tail and the number of degrees of freedom. From that information, qchisq() computes the required x-value to get the specified area in the specified tail with the specified number of degrees of freedom.
Note: Round the numbers to two decimals.
E |
Assault |
Burglary |
Larceny |
Homicide |
Total |
1 |
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2 |
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3 |
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4 |
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Total |
C. (2 points) Write your conclusion using the rejection region method “critical value method” include both statistical and related to the topic of the question (practical) interpretation use the function qchisq() in R
a)
Ho: the occurrence of these types of crime is independent on the city district
Ha: the occurrence of these types of crime is dependent on the city district
b)
TS = 124.404
c)
df = 9
critical value = 21.666
qchisq(0.99,9) [1] 21.66599
since TS > critical value
we reject the null hypothesis
we conclude that there is sufficient evidence that occurrence of these types of crime is dependent on the city district