Assume X is distributed Binomial with 50 trials. You decide to sample from X and get a sample mean of 11 and sample variance of 8. 1. Assume we had sampled 2 observations from X to get those sample characteristics Can we conduct a hypothesis test on the variance? 2. Assume instead we sampled 31 observations from X to get those sample characteristics. At the 10% level of significance, test your belief that the population variance is larger than 7. 3. Solve for the two-sided 95% confidence interval for the population variance. 4. Solve for the one-sided 95% confidence interval for the population variance given the direction set out in number 2