A group of nutritionists is hoping to prove that a new soy bean compound has more protein per gram than roast beef, which has a mean protein content of 20. A random sample of 5 batches of the soy compound have been tested, with the following results:

Protein content: 15, 22, 17, 19, 23

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

a) The observations are from a normally distributed population

b) The mean protein content of the 5 batches follows a normal distribution

c) The variance of the population is known

d) We must assume that the observations come from a normally distributed population AND that the mean content of the sample follows the normal distribution

e) We must assume that the observations come from a normally distributed population AND that the mean content of the sample follows the normal distribution AND that the population variance is known