The intrinsic variations in the measured amount of pollution contained in water samples from rivers and streams in a mining region of West Central United States is known to be a normally distributed random variable with a fairly stable standard deviation of 5 milligrams of solids per liter. As an EPA inspector who wishes to test a random selection of n water samples in order to determine the mean daily rate of pollution within ±1 milligram per liter with 95% con?dence, how many water samples will you need to take? A selection of 6 randomly selected water samples returned a mean value of 40 milligrams per liter and what seems like an excessive variance of 30 (mg/liter)2.
Determine a 95% con?dence interval around this estimate of σ2 and comment on whether or not this value is excessive compared to the assumed population value.