A financial company that acts as a stockbroker is interested in examining the monetary value of the trades it has to process each day. It is known that the value of trades each day follow a Normal distribution for its population distribution, with a mean of 1000 and a standard deviation of 100.

Now the business decides to obtain a new sample of data on the value of trades each day. In the sample of data it has 100 observations, and with a sample mean of 800. The firm wishes to perform a hypothesis test on the population mean to test if the population mean has changed, based on this sample of data.

The firm decides to do a 2 sided hypothesis test at the significance level set at 1%. What is your conclusion on the population mean? Show all the mathematical steps in your calculation at how you arrived at your conclusion, including your method.