In: Statistics and Probability
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. 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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