Question: A nutritional store in the mall is selling "Memory Boosters" which is a concoction of herbs and minerals intended to improve performance. To test the effectiveness of the herbal mix, a researcher obtains a sample of n=25 people and has each person take the suggested dosage each day for 4 weeks. At the end of the four week period, each individual takes a standardized memory test. The scores from the sample produced a mean of M=26 with a sample variance of \[{{s}^{2}}\] =64. In the general population, the standardized test is known to have a mean of \[\mu \] =20.

(a) Do the sample data support the conclusion that the Memory Booster has a significant effect? Test with \[\alpha \] =.05.

(b) Construct 95% confidence interval for \[\mu \].