Suppose the population 10 year cumulative incidence of prostate cancer among 70
ID: 3172875 • Letter: S
Question
Suppose the population 10 year cumulative incidence of prostate cancer among 70 year old men is 0.07. Further, suppose 1000 men, without prostate cancer, aged 50 years were randomly sampled and 20 of them developed prostate cancer within 10 years. Is there evidence to conclude that the cumulative incidence of prostate cancer among 50 year old men differs from that of 70 year old men? a) State the null and (2-sided) alternative hypotheses to address this question. b) Calculate an appropriate test statistic that will reflect the compatibility of the data with the null hypothesis. c) Without using tables, what can you say about the associated p-value? d) Given your answer in part c), is there evidence to conclude that the cumulative incidence of prostate cancer among 50 year old men differs from that of 70 year old men? e) Construct a 95% confidence interval for the population 10 year cumulative incidence of prostate cancer among 50 year old men. f) How do the test statistic you computed in part b) and the 95% confidence interval in part e) provide consistent and complementary information?Explanation / Answer
(a) Ho: p = 0.07 versus Ha: p 0.07
(b)
Data:
n = 1000
p = 0.07
p' = 0.02
Hypotheses:
Ho: p = 0.07
Ha: p 0.07
Decision Rule:
= 0.05
Lower Critical z- score = -1.9600
Upper Critical z- score = 1.9600
Reject Ho if |z| > 1.9600
Test Statistic:
SE = {p (1 - p)/n} = (0.07 * (1 - 0.07)/1000) = 0.0081
z = (p'- p)/SE = (0.02 - 0.07)/0.00806845710157772 = -6.1970
(c) p- value should be close to 0 because z is very small
p- value = 0.0000
Decision (in terms of the hypotheses):
Since 6.1970 > 1.9600 we reject Ho and accept Ha
(d) Conclusion (in terms of the problem):
There is sufficient evidence that p 0.07
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.