Consider a random sample of ten children chosen from the population of infants receiving antacids that contain aluminum. The distribution of plasma aluminum levels is known to be approximately normal; however, its mean µ and the standard deviation s are not known. The mean aluminum level for the sample of ten infants is x_bar= 37.2 µg/l and the sample standard deviation is s = 7.13 µg/l.
What would the 95% confidence interval be if the population standard deviation s was known to be equal to the sample value of 7.13 µg/l, what would the 90% confidence interval for µ have been?