Question

1. Philosophical and health issues are prompting an increasing number of Taiwanese people to switch to a vegetarian lifestyle. A study 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 random samples of 51 female vegetarians and 53 female omnivores yielded the following summary statistics, in grams, on daily protein intake:

Vegetarians: mean = 39.04, standard deviation = 18.82, n = 51

Omnivores: mean = 49.92, standard deviation = 18.97, n = 53

Perform the required hypothesis test at the 1% significance level. Assume equality of variances. Your answer should be a positive number.

What is T = ?

2.

Do the data from the previous question provide sufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ?

• A. At the 1% significance level, there is evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ because the obtained t-value is larger than the critical value.
• B. At the 1% significance level, there is insufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ because the obtained t-value is smaller than the critical value.
• C. At the 1% significance level, there is insufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ because the obtained t-value is larger than the critical value.
• D. At the 1% significance level, there is evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ because the obtained t-value is smaller than the critical value.

3.

Using information from Question 1, determine a 99% confidence interval for the difference between the mean daily protein intakes of female vegetarians and female omnivores.

Vegetarians: mean = 39.04, standard deviation = 18.82, n = 51

Omnivores: mean = 49.92, standard deviation = 18.97, n = 53

What is the Confidence Interval

Answer 1

Let denote mean daily protein intake of Vegetarians and Omnivores respectively.

Assuming equality of variances,

3.