Recall Exercise 8.3.19 about dialysis patients dying of heart attacks. The researchers also looked at patients that had their dialysis done on Tuesday, Thursday, and Saturday and experienced cardiac arrest on the same day they had dialysis. They found that 65 of these events happened on a Tuesday, 68 on a Thursday, and 57 on a Saturday. Do we have convincing evidence that the probability of death is not distributed evenly among the three days? Test as follows: 

a. State the hypotheses in words or in symbols. 

b. Calculate the test statistic, and p-value. 

c. State your conclusion in the context of the research question.

Data from Exercise 8.3.19

Patients with kidney disease often undergo a procedure known as dialysis, which cleans their blood because their kidneys can’t properly do this. This procedure is often done three days per week, with Monday, Wednesday, and Friday often being those days. In terms of dialysis treatments, these days are all the same except for the gap of two off days before the Monday treatment. Does this gap make a difference? Cardiac arrest and sudden death for patients undergoing dialysis for kidney disease are a concern. In recent years, it has been noted that these types of patients are apt to have cardiac arrests on Mondays more often than what would be expected if the three days were equally likely. A study published in Kidney International (Karnik et al., 2001) looked at 205 dialysis patients who had cardiac arrests on Monday, Wednesday, or Friday, the same days they underwent dialysis. They found that 93 of these happened on a Monday, 54 on a Wednesday, and 58 on a Friday. Do we have convincing evidence that the probability of death is not the same among the three days? Test as follows.