**Question: **(10 marks). Can quitting smoking improve oral health condition (which can be measure using Oral Health index) over 12 months? A team of researchers is planning a study to examine this question. Based on the results of a previous study, they are willing to assume a standard deviation of 2 for the percentage change in Oral Health index over the 12 month period. An increase in Oral Health index of 1 percent (effect size) would be considered clinically important. Assuming the data can be considered normally distributed, the researchers will conduct a two-sided test with a Type I error of 5% and are willing to accept a power of 0.80. (Hint: you can use the online Sample Size calculator provided in lecture 2, slide 49).

a. Perform a calculation to determine whether a sample of 30 subjects is a large enough sample to give the required power. (2 marks)

b. Estimate the smallest sample required to give a power of at least 0.9. (2 marks)

c. If Type I error is controlled as 0.01, and power needs to reach 0.9, what is the smallest sample size needed? (2 marks)

d. If I consider 2 percent of change in Oral Health index as clinical importance, given the required type I error as 5% and power as 0.8, what is the sample size needed? (2 marks)

e. How would you interpret the relation between sample size, significance level, power and effect size? (2 marks)