2. What is the required sample size? Please answer the question for the following cases repectively. [8 marks] (a) It has been found that the mean for creativity is 12.85 and the variance is 13.4. A researcher wants to determine the mean number to attend one certain study related to creativity. The error in estimating the mean is to be less than 0.5 with a 98 percent level of confidence. How many articipants are suitable for the study? (b) A research group would like to conduct a mental health study in a small town to determine the mean number of people who have had mental health issues in their life. The error in estimating the mean is to be less than 6.5% with a 90% level of confidence. No estimate of the population proportion exists. What is the size of the sample needed for this study?