A paper described the results of a medical study in which one treatment was shown to be better for men and better for women than a competing treatment. However, if the data for men and women are combined, it appears as though the competing treatment is better.

To see how this can happen, consider the accompanying data tables constructed from information in the paper. Subjects in the study were given either Treatment A or Treatment B, and survival was noted. Let S be the event that a patient selected at random survives, A be the event that a patient selected at random received Treatment A, and B be the event that a patient selected at random received Treatment B.

Answer parts (a) through (e). Round your answers to 3 decimal places.

1(a). The following table summarizes data for men and women combined.

	Survived	Died	Total
Treatment A	212	88	300
Treatment B	247	53	300
Total	459	141

Find P(S):

Find P(S | A):

Find P(S | B):

1(b). Now consider the summary data for the men who participated in the study.

	Survived	Died	Total
Treatment A	120	80	200
Treatment B	20	20	40
Total	140	100

Find P(S):

Find P(S | A):

Find P(S | B):

1(c). Now consider the summary data for the women who participated in the study.

	Survived	Died	Total
Treatment A	92	8	100
Treatment B	227	33	260
Total	319	41

Find P(S):

Find P(S | A):

Find P(S | B):

1(d). Which treatment appears to be better for all patients? ["Treatment A", "Treatment B"]

Which treatment appears to be better for men? ["Treatment A", "Treatment B"]

Which treatment appears to be better for women? ["Treatment A", "Treatment B"]

1(e). You should have noticed from parts 1(b) and 1(c) that for both men and women, the same treatment appears to be better. But in part (a), when the data for men and women are combined, it looks like different treatment is better. This is another example of Simpson's paradox that we have studied in Section 3.1. In a brief explanation, why is this apparent inconsistency occurring for this data set. (Hint: Do men and women respond similarly to the two treatments?)

Group of answer choices

The results are distorted in favor of Treatment B, as women respond to both treatments better than men, but Treatment A was given to far more women than men.

The results are distorted in favor of Treatment A, as women respond to both treatments better than men, but Treatment B was given to far more women than men.

The results are distorted in favor of Treatment A, as women respond to both treatments better than men, but Treatment A was given to far more women than men.

The results are distorted in favor of Treatment B, as women respond to both treatments better than men, but Treatment B was given to far more women than men.