A group of nutritionists is hoping to prove that a new soybean compound has more protein per gram than roast beef, which has a natural protein content of 20. A random sample of 5 batches of the soy compound has been tested, producing protein contents of 15, 22, 17, 18, and 23.

What assumption(s) do we have to make in order to carry out a legitimate test of the nutritionists' claim?

A) The soybean compound samples are independent and come from a normally distributed population.
B) The soybean compound samples are dependent and come from a normally distributed population.
C) The soybean compound samples are independent and come from a uniformly distributed population.
D) The soybean compound samples are dependent and come from a uniformly distributed population.

A legitimate test of whether the new soybean compound has more protein per gram than roast beef requires the assumption that the samples are independent and come from a normally distributed population (option A).

Explanation:

To carry out a legitimate test of the nutritionists' claim that a new soybean compound has more protein per gram than roast beef, we must make specific assumptions about the nature of the soybean compound samples. We should assume that the soybean compound samples are independent and come from a population that follows a normal distribution. This is option A: The soybean compound samples are independent and come from a normally distributed population. This assumption allows for the application of statistical tests such as the t-test or z-test to determine if there is a significant difference between the mean protein content of the soy compound and that of roast beef.

This assumption is necessary because independence ensures that one sample does not influence another, which is a requirement for most parametric tests. The assumption of normality is important because many statistical tests are based on the normal distribution of the data.