1) Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. A study by Lu et. al., published in the Journal of Nutrition, 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 samples of 51 female vegetarians and 53 female omnivores yielded the following summary statistics, in grams, on daily protein intake. Vegetarians Omnivores X1 =39.04 X) =49.92 51 =18.82 57 =18.97 n1 =51 n =53 Do the data provide sufficient evidence to conclude that the mean daily protein intake of female vegetarians and female omnivores differ? Perform the required hypothesis test at the 1% significance level. 2) Refer to exercise 1. Obtain a 99% confidence interval for the difference between the mean daily protein intake of female vegetarians and female omnivores. Interpret your