Question

A police department released the numbers of calls for the different days of the week during the month of​October, as shown in the table to the right. Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis?

Day	Sun	Mon	Tues	We	Thurs	Fri	Sat
Frequency	155	206	220	244	176	215	240

Calculate the test​ statistic,chi squaredχ2.

Calculate the​ P-value.

What is the conclusion for this hypothesis​ test?

What is the fundamental error with this​ analysis?

Answer 1

The Test Statistic is calculated as below. Since the frequencies are considered to be the same, each expected frequency = Sum of observed frequency / 7 = 1456/7 = 208

Day	Sun	Mon	Tues	We	Thurs	Fri	Sat	Total
Frequency	155	206	220	244	176	215	240	1456
Expected	208	208	208	208	208	208	208	1456
(O - E)	-53	-2	12	36	-32	7	32
(O - E)2	2809	4	144	1296	1024	49	1024
(O - E)2/E	13.5048	0.0192	0.6923	6.2308	4.9231	0.2356	4.9231	30.5289

The test statistic, = 30.53 (rounding to 2 decimal places)

The p value for df = n - 1 = 6 for = 30.53 is; p value = 0.0000

Since p value is < Alpha (0.01), Reject H0.

The fundamental error here us that october has 31 days, and therefore there will be 3 days of the week which will have more calls on those days as compared to the other days of the week.