To test whether there is a tendency for cancer patients to hold on to life long enough to survive for a holiday or birthday, researchers gathered data from thousands of cancer deaths and focused on the 2-week periods surrounding Christmas, Thanksgiving, and each patient's birthday. They looked at various sex, race, and age groups separately, as well as all results combined. They also took into account that Jewish patients would not be expected to consider Christmas to be a special day. The null hypothesis states that the overall proportion of cancer patients who die in the week before a special day is 0.5 (the same as the proportion who die in the week following). Of 5,555 women who died within a week of Christmas, 2,766 died in the week before, as opposed to after.
(a) Calculate the sample proportion of women who died in the week before Christmas. (Round your answer to three decimal places.)