Statistics for Business Giloni Midterm II Show Your Work Professor 1) (32 points) Up until recently, your potato chip factory in Los Angeles was producing chips with an average thickness of 1.2 millimeters (1.2 mm). Recently, new manufacturing equipment was introduced and your customers have suddenly started reporting that the potato chips have gotten thinner. Naturally, you are worried about this, so you arrange to have a random sample of 15 chips taken from the population of all chips produced yesterday. The random sample shows an average thickness of 1.05 mm and a standard deviation of .1 mm. a. Assuming that the thickness of the chips is Normally Distributed, construct a 99% confidence interval for the mean thickness of all chips produced yesterday based upon the sample of size 15. (8 points) b. If the average thickness of all chips is still 1.2 mm, how often would such a confidence interval (a 99% confidence interval based upon a random sample of size 15) fail to contain the number 1.2? Assume that the thickness of the chips is Normally Distributed. (8 points) c. Based upon your answers to parts a) and b), is it believable that the average thickness of all chips is still 1.2 mm? Explain your answer if the form of an executive summary. Assume that the thickness of the chips is Normally Distributed. (8 points) d. Would it be correct to say that there is a 1% probability that the average thickness of all chips is 1.2 mm? Explain your answer carefully. Assume that the thickness of the chips is Normally Distributed. (8 points) 2) (40 points) For the situation described in problem 1), suppose is the mean thickness of all chips produced yesterday. You collect another random sample of size 50, which shows an average thickness of 1.1 mm and a standard deviation of .25 mm. a) Test whether is less than 1.2 mm, at level of significance .04. (8 points) b) Based upon your answer to part a), is it possible that is still 1.2 mm? (8 points) c) Compute the p-value. Based upon this, would we be able to conclude that 1.2 if we had performed the Hypothesis Test (using the same sample) at level of significance .001? Explain. (8 points) d) Suppose you want to convince the company that made the new equipment that the equipment is not working properly. In order to make the strongest case possible based upon the given data, you would like to say that you have found an extremely statistically significant decrease in thickness. What is the strongest statement you can make regarding the statistical significance of the decrease? Please write your answer as an executive summary. (8 points) e) To answer questions 2a through 2d, do you need to assume that the thickness of the chips is Normally Distributed? Explain. (8 points) 3) (28 points) For the situation described in problems 1 and 2, suppose that the population standard deviation of the thickness of the chips is =.3 mm. You are going to test HO: =1.2 versus HA: <1.2 with level of significance .03 based upon a random sample of size 200 which has not yet been collected. a) What is the probability that you will correctly decide, based upon the above hypothesis test, that <1.2 if in fact =1.1 ? Show your work and you must give a numerical answer? (10 points) b) What is the probability that you will accept the Null Hypothesis, based upon the above hypothesis test, if in fact = 1.1 ? Show your work and/or explain. You must give a numerical answer? (6 points) c) What is the probability that you will incorrectly decide, based upon the above hypothesis test, that <1.2 if in fact = 1.2 ? Explain. (6 points) d) To answer questions 3a through 3c, do you need to assume that the thickness of the chips is Normally Distributed? Explain. (6 points)