New research has been released, advising that people should eat a mean of 30 grams of protein per day. However, a researcher believes that the population mean is greater than this and tested his belief by taking a random sample of 16 adults. From that sample, the researcher used the mean and standard deviation to find a calculated test statistic of 12.45. Assume the conditions are satisfied, and the population standard deviation is NOT known.

a) Write the hypotheses to test the researcher's belief.

b) Using a 0.01 level of significance, what is the critical value for this test?

c) Give the test decision, briefly explaining your reasoning.

d) Give the test conclusion.

e) Describe a Type I error, in the context of this question.