Question

The police department in Madison, Connecticut, released the following numbers of calls for the different days of the week during a February that had 28 days: Monday (114); Tuesday (152); Wednesday (160); Thursday (164); Friday (179); Saturday (196); Sunday (130). Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. Is there anything notable about the observed frequencies?

Answer 1

Category	Observed Frequency (O)	Expected Frequency (E)	(O-E)²/E
Monday	114	1095 * 1/7 = 156.4317	(114 - 156.4317)²/156.4317 = 11.5095
Tuesday	152	1095 * 1/7 = 156.4317	(152 - 156.4317)²/156.4317 = 0.1255
Wednesday	160	1095 * 1/7 = 156.4317	(160 - 156.4317)²/156.4317 = 0.0814
Thursday	164	1095 * 1/7 = 156.4317	(164 - 156.4317)²/156.4317 = 0.3662
Friday	179	1095 * 1/7 = 156.4317	(179 - 156.4317)²/156.4317 = 3.2559
Saturday	196	1095 * 1/7 = 156.4317	(196 - 156.4317)²/156.4317 = 10.0085
Sunday	130	1095 * 1/7 = 156.4317	(130 - 156.4317)²/156.4317 = 4.4661
Total	1095	1095	29.8131

Null and Alternative hypothesis:      

Ho: Proportions are same.      

H1: Proportions are different.      

Test statistic:      

χ² = ∑ ((O-E)²/E) = 29.81

df = n-1 = 6     

p-value:      

p-value = CHISQ.DIST.RT(29.81, 6) = 0.000

Decision:      

p-value < α, Reject the null hypothesis      

There is enough evidence to reject the claim that the different days of the week have the same frequencies of police calls at 0.01 significance level.

We note that the number of calls on a Saturday appears to be much higher than the number of calls on the other days.