Question

In: Statistics and Probability

Exercise 3 In a study, randomly selected records of 140 crimes reveal that they were committed...

Exercise 3

In a study, randomly selected records of 140 crimes reveal that they were committed on the following days of the week.

Day

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

Number of crime

17

21

22

18

23

24

15

Please answer the following questions underneath each question.

1. Which test is appropriate to to examine whether crimes are equally likely to be

committed on any day

Answer:

2. Conduct the steps of this test

(please enumerate and write all the steps of your answer below)

Step 1:

3. State your conclusion in the context of this study

Solutions

Expert Solution

Answer:

1. Test to be conducted: Chi square test of goodness of fit

Test that is used to find out if the observed value of a given phenomena is significantly different from the expected value

2.

Step 1:

Ho: The proportion of crime commited on all days of the week are equal; i.e. = 1/7

Ha: ​: Some of the population proportions differ from the values stated in the null hypothesis

Step 2: Chi square test stat

Day Observed values
(fo)
Expected Proportions Expected values
(fe)
(fo-fe)2/ fe
Mon 17 0.143 20.00 0.450
Tue 21 0.143 20.00 0.050
Wed 22 0.143 20.00 0.200
Thur 18 0.143 20.00 0.200
Fri 23 0.143 20.00 0.450
Sat 24 0.143 20.00 0.800
Sun 15 0.143 20.00 1.250
Total 140 1.000 140.00 3.400

= 3.40

p value = 0.7572

Step 3:

As the level of significance is not given, taking = 0.05, df = 7

Chi square critical = CHISQ.INV.RT(probability,df) = CHISQ.INV.RT(0.05, 6) = 5.348

Step 4: Decision

As ( 3.40) is less than critical, we fail to reject the Null hypothesis.

Hecne we dont have sufficient evidence to believe that no of crimes committed on differenet days during a week are different.

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