A certain chemical compound (measured in milligrams) is important in a drug used to promote sleeping, but too little and the drug will not be effective, and even a slight overdose could have nasty side effects. The ideal amount of it in each pill is 46mg. A statistician from the FDA is testing a particular drug on the market to see if the average amount is different from 46mg. A sample of 100 pills is collected, and it is found the sample mean ¯x = 48mg and sample standard deviation, s = 7.5mg. A significance level of 99% is desired. (A) State the null and alternate hypotheses. (B) Conduct the hypothesis test. Do you reject or not reject the null? What does it mean in the context of the problem? Should the factory increase or decrease the chemical compound it is putting into its pills? (C) Construct a 99% confidence interval for µ. Can we be 99% confident that the true mean is different from 45mg? Does our conclusion agree with that for our hypothesis test?​