1.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.

2.Say, Apple Inc. claims that 27% of all Apple device users own an iPad. If a random sample of 315 Apple device users is selected, what is the Z score if 37% of those sampled own an iPad?Assume the conditions are satisfied.Give your answer correctly rounded to two decimal places.

3.The production manager at a textile mill, believes that a new machine, producing cloth, is not workingaccording to the company's specifications.The company requires that the cloth should have a mean breaking strength of 38 Kg.A sample of 91 pieces of cloth reveals a sample mean breaking strength of 39.2 Kg and a standard deviation of 0.5 Kg.If the manager wants to do a hypothesis test to her belief, what value of the mean would be used in the null and the alternative hypotheses?