Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper "LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores" (Journal of Nutrition, Vol. 130, pp. 1591-1596), S. Lu et al. compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan. Among the nutrients considered was protein. Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. Independent random samples of 51 female vegetarians and 53 female omnivores yielded the data, in grams, on daily protein intake presented on the WeissStats CD. Use the technology of your choice to do the following.
a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples.
b. Do the data provide sufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ? Perform the required hypothesis test at the 1% significance level.
c. Find a 99% confidence interval for the difference between the mean daily protein intakes of female vegetarians and female omnivores.
d. Are your procedures in parts (b) and (c) justified? Explain your answer.