Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences. The recommended dietary allowance (RDA) of iron for adult females under the age of 51 is 18 milligrams (mg) per day. The following iron intakes, in milligrams, were obtained during a 24-hour period for 45 randomly selected adult females under the age of 51.

At the 1% significance level, do the data suggest that adult females under the age of 51 are, on average, getting less than the RDA of 18 mg of iron? Assume that the population standard deviation is 4.2 mg. (x-bar = 14.68 mg.)

15.0 18.1 14.4 14.6 10.9 18.118.2 18.3 15.0 16.0 12.6 16.6 20.7 19.8 116 12.8 15.6 110 15.3 94 19.5 18.3 14.5 16.6 11.5 16.4 12.5 14.6 11.9 12.5 18.6 13.1 12.1 10.7 17.3 124 17.0 63 16.8 12.5 16.3 14.712.7 16.3 115