A company that manufacturers coffee for use in commercial machines monitors the caffeine content in its coffee. The company select 25 samples of coffee every hour from its production line and determines the caffeine content. From historical data, the caffeine content in milligrams is known to have a normal distribution. During a 1-hour time period, the 25 samples yielded an average caffeine content of 110 mg and standard deviation 7.1 mg. Use the sample information to calculate 90% and 98% confidence intervals for the mean caffeine content of the coffee produced during the hour in which the 25 sample were selected.
What is the lower limit of the 90% interval? Give your answer to two decimal places.
What is the upper limit of the 90% interval? Give your answer to two decimal places.
What is the lower limit of the 98% interval? Give your answer to two decimal places.
What is the upper limit of the 98% interval? Give your answer to two decimal places.
In the next hour, the company wishes to construct a 95% confidence interval of the average caffeine with margin of error m = 3 mg. How many samples of coffee should the company select?
In the next hour, the company wishes to construct a 99% confidence interval of the average caffeine with margin of error m = 3 mg. How many samples of coffee should the company select?