New research has been released, that adults should get a mean of 7 hours of sleep per night. A sleep therapist claims the population mean is greater than this and tested her belief by taking a random sample of 36 adults. From that sample, the sleep therapist used the mean and standard deviation to find a calculated test statistic of 3.85. Assume the conditions are satisfied, and the population standard deviation is NOT known.

a) Write the hypotheses to test the sleep therapist's claim.

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 II error, in the context of this question.