An obstetrician maintains that preterm babies (gestation period less than 37 weeks) have a higher variability in birth weight than do full-term babies (gestation period 37 to 41 weeks). According to the National Vital Statistics Report, the birth weights of full-term babies are normally distributed, with standard deviation 505.6 grams. A random sample of 41 preterm babies results in a standard deviation equal to 840 grams. Test the researcher's hypothesis that the variability in the birth weight of preterm babies is more than the variability in birth weight of full term babies, at the a = 0.01 level of significance.