1. Suppose we have a sample with a sample mean of 30 and we know the population standard deviation is 10. Construct 90%, 95% and 99% confidence intervals for the population mean using different sample sizes of 30, 60 and 100. Fill in the following table to answer the following questions: (10 Points) Sample Size 90% 30 60 Confidence Intervals 95% 99% 100 a) For all sample sizes, what happens to confidence intervals as we increase the confidence level? (i.e. move from left to right for each row) b) For all confidence levels, what happens to confidence intervals as we increase the sample size? (i.e. move down for each column)