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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 working according 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?

Let that across the two semesters of this statistics course, you have been shown both Bayesian and Classical approaches to Inference. A fellow student in a biological sciences course is working with statistics, but does not understand the two approaches. Provide them with a short explanation of the differences and similarities between the approaches, to help them with their use of statistics. {approx. 500 words}. 4. Exercise 19 a and b, Chapter 2. Exponential model with conjugate prior distribution: a. Show that if y 0 is exponentially distributed with rate 0, then the gamma prior distribution is conjugate for inferences about 0 given an independent and identically distributed sample of y values. b. Show that the equivalent prior specification for the mean,d = 1/0 is inverse-gamma. (That is, derive the latter density function.)Assignment 4: Bayesian Networks and HMM / 3. Question 3: Bayes inference saved Given the Bayes Network specified below, calculate the probability P(A B). Make sure to write out your full answer. Assume that P(A) 0.3. P(DIA) = 0.7 P(D| ~ A) = 0.5 P(B A) = 0.2 P(B| ~ A) = 0.6 B D P(C B) = 0.7 P(C| ~ B) = 0.7