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# ENMGT 572 Managerial Statistics Exam I 1. USFEC rents the flatbed trailers on which the organizations participating in the parade build their floats....

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ENMGT 572 Managerial Statistics Exam I 1. USFEC rents the flatbed trailers on which the organizations participating in the parade build their floats. The company that owns these trailers determines their rental price based on the mean weight of a parade float. The standard deviation of float weight is widely known to be 125 pounds. The types of floats used in the Martinsville parade typically fall into the second classification on the company’s pricing scale. This classification places an upper limit of 850 pounds on the mean. Therefore, USFEC wishes to perform hypothesis test about the mean weight of a parade float using a level of significance of 0.1. Furthermore, USFEC wishes to detect a true mean of 900 pounds with probability 0.95. (a) What sample size should USFEC use? (b) State the null and alternative hypothesis. What is the critical region for this test? (c) What is the power of this test if the true mean float weight is 885 pounds? (d) If the sample size computed in part (a) is used and the resulting sample mean is 868 pounds, then what is the value of the test statistic and the corresponding conclusion for the test? (e) What is the smallest level of significance that would have resulted in rejecting the null hypothesis? 2. P2_Data sheet on the exam template contains market research information of 2000 customers who shop at a local drug store. The store is interested in the customers buying preferences of toothpaste. Assume that this data represents the population. (20 points) a. What is the population mean and standard deviation for the proportion of customers who use Crest toothpaste? b. Using the data, select the first 200 customers as sampling data. Of these 200 samples, compute a point estimate and standard error of the portion of customers who prefer crest toothpaste c. Using the sample data in part b, of these 200 samples, what is the 95% confidence intervals for this sample proportion data d. Using the sample data in part b, conduct a two sided hypothesis test to determine if the sample point estimate is equivalent to the population proportion value. Conduct this test at alpha equal to .01 3. An article in Food Testing and Analysis, “Improving Reproducibility of Refractometry Measurements of Fruit Juices” (1999, V4, pp 13-17) measured the sugar concentration (Brix) in clear apple juice. All readings were taken at 20 o C: a. The research team was interested in finding if the true mean concentration is 11.5 at a level of significance of a =0.05. Using the P-value determine the conclusion of the research team about the mean concentration. Clearly state your null and alternative hypothesis. b. Compute the power of the test if the true mean is 11.4.
ENMGT 572 Managerial Statistics Exam I c. What sample size would be required to detect a true mean sugar concentration of 11.45 if we wanted the power of test to be at least 0.9? d. Explain and calculate how question in part (a) could be answered by constructing the appropriate confidence interval on the mean sugar concentration. 4. Problem 4 (P4 on the Exam template) contains data of the amount that customers spend in a supermarket on a specific Friday. Assume this data represents the population. (10 points) a. What sample size would be required to be 95% sure that the estimate is within + \$10? b. How would the sample size value change for a one sided interval (+\$10) c. Use the data from the first 30 customer to create a sample n = 30. What is the 95% confidence interval for this sample data? d. What is a generic 95% confidence interval for any sample n=30? 5. Marty’s Burger Barn provides a “Be A Glutton” option for all of their combo meals. This option is offered to all customers purchasing a combo meal for an additional charge of \$0.35. Marty has determined that if a store is marketing the option properly, at least 70% of eligible customers will choose to “Be A Glutton”. Marty has asked for your help in evaluating the “Be A Glutton” performance at one of his locations. You have informed Marty that you intend to use a level of significance of 0.05 and that the appropriate confidence interval on p is guaranteed to have an error of 0.02 or less. (a) What sample size will you use? You may assume that this sample size is used for the remainder of the problem. (b) What is the probability of a Type II error when p = 0.65? (c) Explain your answer to part (b) to Marty. Remember that he has no training in probability and statistics. (d) After collecting appropriate data, you find that 1148 customers chose to “Be A Glutton”. Compute P-value and determine the conclusion of the test. (e) Build the 99% confidence interval that is appropriate for this test. 6. Consider the file data on Taxes that is included in worksheet P2 on the exam template. This data represents property taxes paid by 170 residents that live in a small town. Assume this file to be the entire population. Answer the following questions : (20 pts) a. A local politician in this town has stated that the average property taxes are \$1800 and most people do not pay more than this amount. Conduct a test at the α = .01 level to determine if this is true. Note, you want to have strong evidence to disclaim his hypothesis. Therefore, the burden of proof is placed on the politicians claim b. Find the probability of a Type two error when U = 2200
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