please answer the following :)

12. It is currently accepted that "there is no relationship between vaccines and autism rates in children" (www.cdc.gov). Nevertheless, there remains debate on this topic and numerous studies are conducted each year to investigate the relationship between vaccines and other health problems. A sample of children with autism will be surveyed. a. (5 points) This debate is a serious one and we want to minimize the chance of committing a Type-1 error. Will you decide to use a larger level of significance (a = 0.1) OR a smaller level of significance (a = 0.01)? State the level of significance you would use and explain why you answered the way you did. b. (5 points) If the proportion of vaccinated children with autism in the population is estimated to be 1/1,000 (www.nejm.org), show how you would determine the minimum number of vaccinated children with autism that must be surveyed to ensure the sampling distribution of vaccinated children is approximately normal? As part of your answer, state the minimum sample size necessary to assume normality. 13. (5 points) Explain how the t-distribution (not the value of t) changes as degrees of freedom decrease