A study was performed in Basel, Switzerland, on relationship between concentration of plasma antioxidant vitamins and cancer risk. Table shows data for plasma vitamin-A concentration for stomach cancer cases as well as controls.
Stomach-Cancer cases: Mean: 2.65, Standard Error: 0.11, n = 20
Controls: Mean= 2.88, n= 2421
a. If you suppose that the mean plasma vitamin-A concentration among controls is known without error, then what procedure can be employed to test if the mean concentration is the same for stomach-cancer cases and controls? State its hypothesis.
b. Perform the appropriate test for question (a), and make decision with critical value at alpha = 0.05
c. Construct a 95% confidence interval estimate for the mean of vitamin-A concentration in patients with stomach cancer.
d. Repeat the questions (b) and (c) with appropriate tests by supposing n = 60 for stomach cancer cases.