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 s = 7.1 mg. During a 1-hour time period, the 50 samples yielded a mean caffeine content of y(bar) =110 mg. The engineer in charge of the coffee manufacturing process examines the confidence intervals for the mean caffeine content calculated over the past several weeks and is concerned that the intervals are too wide to be of any practical use. That is, they are not pro- viding a very precise estimate of m.
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What would happen to the width of the confidence intervals if the level of confidence of each interval is increased from 95% to 99%?
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What would happen to the width of the confidence intervals if the number of samples per hour was increased from 50 to 100?