A low-level CDC bureaucrat wants to please his boss by gathering evidence that the current government mandated shut down of society is not causing people's mental health to deteriorate, so that it can...

A low-level CDC bureaucrat wants to please his boss by gathering evidence that the current government mandated shut down of society is not causing people's mental health to deteriorate, so that it can safely be continued for several years if the expert says is necessary. He pulls a random sample of 1600 citizens, Gathering data on such items as income loss, weight gain, access to toilet paper, our spent binge watching Netflix, and number of injuries caused by household fight, and compiles all this into a significantly-weighted "misery index". The mean misery index from the sample is 99.2; it seems reasonable to use a population standard deviation o=19.1.

A. Does this information provide significant evidence (at the 5% level) that the Nationwide mean misery index is less than 100? Set up appropriate null and alternative hypothesis, calculate the appropriate test statistic, find the p-value, and state your conclusion.