Nature lovers' association of Australia, launched a campaign to encourage paper less communication and/or recycling of used papers to save the trees to reduce global warming. Hence, many small businesses have scaled up their business such as new forms of online document exchanges and collecting used papers and cardboards from households and companies.

Abita Recycling Ltd is one such company which is operates in Melbourne. The financial analysist of the company has estimated that the firm would make a profit if the mean weekly collection of papers and cardboards from each household exceeded 1KG. To examine the feasibility of a recycling plant, a random sample of 100 households was selected and sample mean and standard deviations are 1.1KG and 0.35KG respectively.

Following the 6-step process of hypothesis testing, you are required to examine do this information provide sufficient evidence at 99% confidence to allow the analyst to conclude that a recycling plant would be profitable?

(Note: please explain it with details information with formulas, so I can clearly understand, many thanks in advance)