1) For a subset of patients it has been shown that a certain type of skin lesion will develop into cancer in 34% of patients if left untreated. There is a drug on the market that currently reduces this event rate to 28%.A pharmaceutical company is developing a new drug to treat these lesions but this would be worthwhile only if the new drug can reduce this further to 23%.In planning for a randomized clinical trial, how many evaluable participants are needed to have 80% power to detect a difference of 28% and 23% in the progression to cancer between the current and new drug?

2) Researchers are interested in reaction times under two conditions. A prior study reported reaction times of 12 minutes and 15 minutes for the two conditions with a common standard deviation of 10. How many experimental units should be used in the study to have 80% power to detect a similar difference? Assume a 5% level of significance.

3) How does the effect size affects the power of a test? Provide an example along with your explanation.