Problem 7. (7 points) A random sample of 120 observations produced a mean of 24 from a population with a normal distribution and a standard deviation of 3.03. Find a 90% confidence interval for M: OSUS[ Note: Round your answer to 2 decimal places. Note: You can earn partial credit on this problem.Problem 8. (7 points) A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 30 ounces. The distribution of weights is known to be normal with standard deviation 1.2. A random sample of 29 boxes yielded an average weight of 30.5 ounces. Suppose an inspector wants to test the null hypothesis that the population mean weight is at least 30 ounces. That is, test the null hypothesis Ho : H = 30 against the alternative hypothesis Ha : H