Sample size and power considerations: What sample size do you need for each of the following investigations? Explain your work fully in the context of the study. For each case, interpret what the effect size means. It is always a good practice to deliberate the "practical" significance of the difference being tested as well as feasibility of implementing the calculated sample size. In other words, the sample size obtained is a mere number based on a formula. It may be too large to be practically implemented or too small to discover anything meaningful. Explain what you would recommend or fix for each case.

(a) There was a speculation that the average income of university freshmen in Canada is less than $20,000. Investigators at a survey company set out to find the truth. To get some ideas about the necessary ingredients for the sample size formula, they collected trial data and found that the mean income was $14,500 with standard deviation of 6000.

(b) You are interested in determining if the average protein level in blood is different between men and women. You collected the following trial data on protein level (grams/deciliter). Male Protein 1.8, 5.8, 7.1, 4.6, 5.5, 2.4, 8.3, 1.2 Female Protein 9.5, 2.6, 3.7, 4.7, 6.4, 8.4, 3.1, 1.4 1