Correct statistical test to compare multiple rates


I am trying to determine whether the risk of dying on any one day is higher than other days for patients in hospital.

I have calculated the number of deaths that occurred on each day of the week (which is acting as my denominator) and have calculated the number of days that a patient is exposed (as my numerator).

For example, of approximately 200 patients, 35 died on a Monday. In total, patient's who died experienced 380 Mondays. Therefore on a Monday, for every 10.86 days, there is one death (380/35). I have calculated this for every day of the week, and I want to do a test to see whether there is a difference in numbers across all days.

I welcome alternative approaches too if people think the above is not right.

Any help is much appreciated! (I plan to use SPSS or excel for the calculation)