Question

4-5. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery (group 1), 9 eventually died of prostate cancer compared with 31 of the 348 men (group 2) who did not have surgery. The researchers want to determine if surgery increases the chance of survival. Let p1: proportion of men that survived after surgery and p2: proportion of men that survived without surgery.

4. Construct a two-tailed 95% confidence interval for the difference between men’s survival without and with surgery and interpret it in terms of the problem context.

a. Justify assumptions for your CI.

b. Compute the 95% confidence interval and interpret it:

5. Apply a Hypothesis testing.

a. What are the null and alternative hypotheses?

b. Justify the assumptions before you compute your test statistic and then compute the test statistic.

c. What is the p-value for this test?

d. What would you conclude from this test at 5% level of significance?

Answer 1

4)

a)

Total number of sample 1 (n1) = 347

Total number of sample 2 (n2) = 348

number of favourable events (X1) = 9

number of favourable events (X2) = 31

Confidence interval(in %) = 95

z @ 95% = 1.96

b)

Since we know that

Required confidence interval = (-0.063-0.0343, -0.063+0.0343)

Required confidence interval = (-0.0973, -0.0287)

5)

Total number of sample 1 (n1) = 347

Total number of sample 2 (n2) = 348

number of favourable events (X1) = 9

number of favourable events (X2) = 31

a) We are interested in testing the hypothesis

b)

c) Since P-value of a two tailed test is equal to

P = (0.0001768622861287863)

P = 0.0002

d)

Here, the P-value is less than the level of significance 0.05; reject the null hypothesis

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.6448536269514722 or greater than the critical value 1.6448536269514722

The statistic value, -3.5724 is less than the critical value -1.6448536269514722. Hence, reject the null hypothesis.

The researchers claim that surgery increases the chance of survival is true

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