Question: Vitamin \[{{B}_{6}}\] is one of the vitamins in a multi-vitamin pill manufactures by a pharmaceutical company. The pills are produced with a mean of 50 milligrams of vitamins \[{{B}_{6}}\] per pill. The company believes that there is a deterioration of 1 milligrams per month, so after 3 month they expect that \[\mu \] =47. A consumer group suspects that the mean is actually much less, and decide to conduct a test.

Based on a random sample of size 24 from a normal distribution, the data gives \[\bar{x}\] =45.6615 and \[{{s}^{2}}\] =26.7855

a. Construct a 99% confidence interval for the standard deviation of the amount of \[{{B}_{6}}\] per pill.

b. Test \[\mu \] =47 versus \[\mu \] <47 at the 1% significance level. Clearly state the conclusion.