A company that manufacturer's coffee for use in commercial machines monitors the caffeine content in its coffee. The company selects 50 samples of coffee every hour from is production line and determines the caffeine content. From historical data, the caffeine content (in milligrams, mg) is known to have a normal distribution with sigma= 7.1 mg. During a 1- hour time period, the 50 samples yielded a mean caffeine content of (y with line on top)= 110 mg.
a. Calculate a 95% confidence interval for the mean caffeine content mew of the coffee produced during the hour in which the 50 samples were selected.
b. Calculate the test statistic z
c. What are the conclusions of the test if the error level is alpha=0.05? what type of error may have occurred?
d. What are the conclusions of the test if the error level is alpha=0.01? what type of error may have occurred?