. A nutrition store in the mall is selling \"Memory Booster," which is a concoction of herbs and minerals that is intended to improve memory performance, but there is no good reason to think it couldn't possibly do the opposite. To test the effectiveness of the herbal mix, a researcher obtains a sample of 8 participants and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes a standardized memory test. In the general population, the standardized test is known to have a mean of u = 7. (Set the signicance level 9 a. = .05) (10 points) 6. It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test to show that only children have an average higher cholesterol level than the national average. We test 100 only children and find out the mean is 198. You can use your own confidence level. (All Americans Standard Deviation is 15) (10 points)5. Believe it or not, there are some people who don't think that Duke will win the NCAA tournament this year. Let's say that you want to measure the average intelligence of Duke Doubters. Problem is you could only nd 28 DDs on this whole campus. The mean of your sample was 90 and the standard deviation was 60. Calculate the 90% Condence Interval for the IQ of DDs. (10 points)