More than 16,000 older women were asked to wear a device to record their steps per day over the course of a week, and the women were then divided into quartiles based on the number of steps per day. The researchers tracked the women and recorded how many died, of any cause, during a follow-up period of about five years. The results, as well as the median number of steps per day for each quartile, are shown in Table 4.11. We test to see if even increasing steps a small amount (from the amount in one quartile of the sample to the next higher quartile) gives a significant decrease in mortality.

(a) Conduct a difference in proportions test to see if the proportion dying is higher in women who walk at the level of Quartile 1 compared to women who walk at the level of Quartile 2. 

(b) Repeat part (a) using Quartiles 3 and 4. Use a significance level of 5%. 

(c) The title of this problem appears to imply causation. Is that appropriate here? Why or why not?

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Table 4.11 Steps per day and mortality Number of Deaths 275 103 Quartile Median Steps 2718 4363 1234 5905 8442 77 49 Number of Women 4185 4185 4186 4185