The makers of an exercise device advertise that using their machine a few minutes per day results in an average weight loss of 4 kilograms during the first month. A consumer group believes the average weight loss would be less than this. The consumer group recruited 36 volunteers to use the product in accordance with the manufacturer's recommendations. They found an average weight loss of 3.2 kilograms with a standard deviation of 1.8 kilograms. You are told that the calculated test statistic is 2.67. Assume the conditions are satisfied.

a) Write the hypotheses to test the consumer group's claim.

b) Give the critical value if testing at the 1% level of significance.

c) Give your decision and briefly explain your reasoning.

d) Give your conclusion with respect to the consumer group's claim.

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