Please solve it with all processes, and add detailed explanations to each step(theorems or formulas has been used). Thanks!

2. A newspaper journalist is investigating 'BetterCaf', a high-street coffee chain. The jour- nalist has received a number of health concerns by BetterCaf's customers where they believe that the decaffeinated coffee contains a higher concentration of caffeine than what the chain claims. On their website, BetterCaf states that the expected caffeine concentration in their decaffeinated coffee is 15 ug/ ml. To investigate, the journalist pur- chases a decaffeinated coffee at 8 BetterCaf cafs and send a sample of each to a lab for analysis. The lab report states that the average caffeine content across the samples is 21.4 ug/ ml with a standard deviation of 9.3 pig/ml. The journalist approaches you to interpret the lab report into whether there is any evidence to substantiate the claims made by BetterCaf's customers. Perform an appropriate hypothesis test at the 5% signicance level. Clearly state your hypotheses, all denitions and any assumptions you have made in your investigation