A company that manufacturers coffee for use in commercial machines monitors the caffeine content in its coffee. The company selects 50 samples of coffee every hour from its production line and determines the caffeine content. From historical data, the caffeine content (in milligrams, mg) is known to have a normal distribution with σ = 7.1 mg Π. During a 1-hour time period, the 50 samples yielded a mean caffeine content of y-bar = 110 mg.
a. Identify the population about which inferences can be made from the sample data.
b. Calculate a 95% confidence interval for the mean caffeine content m of the coffee produced during the hour in which the 50 samples were selected.
c. Explain to the CEO of the company in nonstatistical language the interpretation of the constructed confidence interval.