Question

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

Answer 1

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.