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. 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). They looked at various sex, race, and age groups separately, as well as all results combined. Of 6,968 elderly (at least 70 years old) cancer patients who died within a week of their birthday, 3,547 died in the week before, as opposed to after.
a. Calculate the sample proportion of elderly patients who died in the week before their birthday.
b. If we use a one-sided alternative hypothesis Ha : p 0.5 to claim that, in general, people hold on to life in order to survive a holiday, does the sample proportion tend in the right direction to support this claim?
c. The standardized sample proportion is z 1.51. If we test H0 against the twosided alternative Ha : p 0.5, use the 68-95-99.7 Rule to tell which of these intervals reports the correct range for the P-value: less than 2(0.0015), between 2(0.0015) and 2(0.025), between 2(0.025) and 2(0.16), greater than 2(0.16).
d. Use a 0.05 as the cutoff for what we would consider to be a "small" P-value. Which one of these is the correct conclusion to draw from the results of testing against the two-sided alternative:
1. There is no convincing evidence that proportion of all elderly cancer patients dying before their birthday differs from 0.5.
2. There is convincing evidence that proportion of all elderly cancer patients dying before their birthday differs from 0.5.
3. Elderly cancer patients tend to hold on to life until after their birthday.
e. In this problem, should we denote 0.5 as , p, or p0?