Question

At an emergency room at one hospital, the nurses are convinced that the number of patients that they see during the midnight shift is affected by the phases of the moon. The doctors think this is an old wives’ tale. The nurses decide to test their theory at the 0.10 level of significance by recording the number of patients they see during the midnight shift for each moon phase over the course of one lunar cycle. The results are summarized in the table below. Perform a test for goodness of fit.

ER Patients During the Midnight Shifts :Number of Patients: New Moon 85 ,1st Quarter 66 ,Full Moon 97, 3rd Quarter 68

Answer 1

Hypotheses are:

H0: The number of patients does not affect by the phases of the moon.

Ha: The number of patients affected by the phases of the moon.

Total number of paitents = 85 +66 +97 +68 = 316

Since number of patients are uniformly distributed between four phases so number of patients in each phase is

E = 316 / 4 = 79

Following table shows the calculations for goodness of fit test;

O	E	(O-E)^2/E
85	79	0.455696203
66	79	2.139240506
97	79	4.101265823
68	79	1.53164557
Total		8.227848101

Following is the test statistics:

Degree of freedom: df = 4-1 = 3

The p-value is: 0.0415

Conclusion: Since p-value is less than 0.10 so we reject the null hypothesis. That is we can conclude that the number of patients affected by the phases of the moon.

Excel function used for p-value: "=CHIDIST(8.228, 3)"

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