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In: Math

A criminologist conducted a survey to determine whether the incidence of certain types of crime varied...

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.

  1. (1 point) State the two hypothesis of interest.
  1. (2 points) Calculate an appropriate test statistic for (a) by hand. Use the table below to do the calculations of the expected frequencies.

Note: Round the numbers to two decimals.

E

Assault

Burglary

Larceny

Homicide

Total

1

2

3

4

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

Solutions

Expert Solution

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

milcah answered 8 months ago
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