A bottling and packaging company is researching their filling machines to ensure proper procedures. As empty bottles come through on a conveyer belt, the machine will automatically fill them up with the product and send them off to the final packaging stage.

Management has determined that $36\mathrm{.}4$ ounces is the optimal amount of product that the bottles can hold $($anything more than that will cause the bottles to overflow and anything less will not be fair to the customer$).$ Assume that the sample size is $100.$

Required:

Assuming that the population standard deviation is $2\mathrm{.}1$ ounces, test at $5$ percent level of significance if management has anything to worry about.