Men with prostate cancer were randomly assigned to undergo surgery, or “watchful
ID: 3177333 • Letter: M
Question
Men with prostate cancer were randomly assigned to undergo surgery, or “watchful waiting”(WW). The results over the next several years are found below:
Assume we want to test if death was independent of what group they were in (Surgery, WW) with = 0.05.
(a) State the appropriate null hypothesis.
(b) State the appropriate alternative hypothesis.
(c) Calculate the test-statistic.
(d) Find the range for the p-value.
(e) State your decision. Did you reject, or fail to reject the null?
(f) State your conclusion in terms of the problem.
(g) What was the sample estimate of the probability of
death, if you were in group Surgery?
(h) What was the sample estimate of the probability of death, if you were in group WW?
Explanation / Answer
a)here null hypothesis: death is independent of group
b)alternate hypothesis: death is dependent of group
c)
chi square test stat =3.754
d) p value =0.0527
e)fail to reject as p vlaue is higher then 0.05.
f)we do not have sufficient evidence to conclude that death depends on groups.
g)probability =83/(83+264)= 0.2392
h)probability =106/(106+242)=0.3046
Observed O surgery WW Total died 83 106 189 alive 264 242 506 Total 347 348 695 Expected E=rowtotal*column total/grand total surgery WW Total died 94.364 94.636 189 alive 252.636 253.364 506 Total 347 348 695 chi square =(O-E)^2/E surgery WW Total died 1.369 1.365 2.733 alive 0.511 0.510 1.021 Total 1.880 1.874 3.754