A manufacturer of pharmaceutical products analyzes each batch of a product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise. In fact, repeated measurements follow a Normal distribution with mean equal to the true concentration and with standard deviation grams per liter(g/l). Three random samples of one batch are taken and the analyses give concentrations of 0.8403, 0.8363, and 0.8447 g/l.

a) Estimate the true concentration using a 95% confidence interval for . Follow the four-step process in formulating your response.

Here are three confidence intervals from the same data with varying confidence levels: (0.83032, 0.85055), (0.83540, 0.84546), and (0.83398, 0.84689).

i) Three confidence levels were used: 80%, 90% and 99%. Which of these three intervals is the 99% confidence interval? Which one is the 80% confidence interval? Explain your reasoning.

ii)Which of these three intervals is the narrowest? Explain why the narrowest interval in this set is not necessarily the most informative.

c) How many measurements would be needed to estimate the true concentration within ±0.001 g/l with 95% confidence?

d) How many measurements would be needed to estimate the true concentration within ±0.001g/l with 99% confidence? What is the implication of choosing a higher confidence level?