Question

Problem: Proportion of ”Cured” Cancer Patients: How Does Canada Compare with Europe?

Lung cancer remains the leading cause of cancer death for both Canadian men and women, responsible for the most potential years of life lost to cancer. Lung cancer alone accounts for 28% of all cancer deaths in Canada (32%. in Quebec). Most forms of lung cancer start insidiously and produce no apparent symptoms until they are too far advanced. Consequently, the chances of being cured of lung cancer are not very promising, with the five-year survival rate being less than 15%. The overall data for Europe show that the number of patients who are considered ”cured” is rising steadily. For lung cancer, this proportion rose from 6% to 8%. However, there was a wide variation in the proportion of patients cured in individual European countries. For instance, the study shows that for lung cancer, less than 5% of patients were cured in Denmark, the Czech Republic, and Poland, whereas more than 10% of patients were cured in Spain.

3. To test the claim regarding proportion of cured cancer patients in Spain, a random sample of 500 patients yielded 39 who were cured.

(a) State the appropriate null and alternative hypotheses.

(b) Calculate the value of the test statistic.

(c) Calculate the p-value and write your conclusion.

Answer 1

From the given information,

n= 500

p= 39/500 = 0.078

Hence,

a. Hypotheses:-

Null hypothesis (Ho): P≤0.10

Alternative hypothesis (Ha): P>0.10

b. By using calculator,

Test statistic= -1.6398

c. By using P-value calculator,

P-value= 0.0505

As P-value > 0.05(Level of significance)

We fail to reject null hypothesis.

Hence, We can conclude that,

There is not sufficient evidence to support the claim that more than 10% of patients were cured in Spain.

Thank you.