A group of nutritionists is hoping to prove that a new soybean 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 has 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?

1. We must assume that the observations come from a normally distributed population and that the mean content of the sample follows the normal distribution.

2. The variance of the population is known.

3. The mean protein content of the 5 batches follows a normal distribution.

4. The observations are from a normally distributed population.

We must assume that the observations come from a normally distributed population, that the mean content of the sample follows the normal distribution, and that the population variance is known.

In order to carry out a legitimate statistical test of the nutritionists’ claim, we must assume that the observations come from a normally distributed population and that the mean content of the sample follows the normal distribution.

The observations must also be from a normally distributed population. Hence, the correct option is: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. To test whether the mean protein content of the soy compound is greater than that of roast beef, we need to carry out a hypothesis test. Since the sample size is less than 30, we need to assume that the population is normally distributed.The assumption that the mean content of the sample follows the normal distribution is necessary to apply the Central Limit Theorem (CLT) and the assumption that the observations are from a normally distributed population is necessary to carry out the hypothesis test.

Finally, in the assumption, the population variance is known, but it is not actually necessary since we can estimate the variance using the sample variance. Therefore, the correct option is:We must assume that the observations come from a normally distributed population AND that the mean content of the sample follows the normal distribution.

To know more about normally distributed population:

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