Consider a population having a standard deviation equal to 10. We wish to estimate the mean of this population.
a. How large a random sample is needed to construct a 95 percent confidence interval for the mean of this population with a margin of error equal to 1?
b. Suppose that we now take a random sample of the size we have determined in part a. If we obtain a sample mean equal to 295, calculate the 95 percent confidence interval for the population mean. What is the interval's margin of error?