Question

Hi, could anyone explain to me how to do these questions? I'm a little confused.

(15 points) 1. The FBI compiles data on robbery and property crimes and publishes the information. A ran- dom sample of pickpocket offenses yielded the losses, in dollars, described by the following summary statistics: x = 513.32, s = 262.23, and n = 20. We want to use this data to make inference on u, the mean loss in all pickpocket offenses in the U.S. Assume a = 0.05 and the data comes from a normal distribution with unknown variance, answer the questions below: (3 points) (a) Construct a CI for . (2 points) (b) If we were to test Ho : y = 398 vs. Hy : u + 398, would we reject or accept the null? Briefly explain your answer. (5 points) (c) Suppose you are told that the population standard deviation is 258. What test statistic would you use now to test the hypotheses in the previous part? Perform the test. Does it contradict the answer in the previous part? (5 points) (d) Using the population standard deviation, and suppose the true mean is 402, what is the probability of Type II error for the hypothesis test in part (b)? (11 points) 2. An engineer measured the Brinell hardness of 25 pieces of ductile iron that were subcritically annealed. The resulting data were computed: Sample size Sample mean Sample variance 25 175.52 10.31 Table 1 (2 points) (2 points) (2 points) (3 points) (2 points) The engineer hypothesized that the mean Brinell hardness of all such ductile iron pieces is greater than 170. Answer the questions below: (a) State the test statistic we need to use to test his/hers hypothesis. (b) State two assumptions you would need to perform the inference. (c) State the null and alternative hypotheses. (d) Construct a 90% CI. (e) Does the CI provide evidence to support the engineer claim? Explain your answer.

Answer 1