Statistics Section II Part B

STATISTICS FREE-RESPONSE QUESTIONS STATISTICS SECTION II Part B Question 6 Spend about 25 minutes on this part of the exam. Percent of Section II score-25 Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 6. Corn tortillas are made at a large facility that produces lines. The distribution of the diameters of the tortillas each 15 its two production normal with mean 5.9 EWO on and the distribution of the diameters of the tortillas produced on normal with mean 6.1 inches. The figure below shows the distributions of diameters for the Production Line A Production Line B 5.7 5.8 5.9 6.0 6.1 6.2 6.3 Diameter (inches) The tortillas produced at the factory are advertised as having a diameter of 6 inches. For the purpose of quality control, a sample of 200 tortillas is selected and the diameters are measured. From the sample of 200 tortillas, the manager of the facility wants to estimate the given day. Two sampling methods have been proposed. of the 200,000 tortillas produced on a : Take a random sample of 200 tortillas from the 200,000 tortillas produced on a given day. Measure the diameter of each selected tortilla. : Randomly select one of the two production lines on a given day. Take a random sample of 200 tortillas from the 100,000 tortillas produced each selected tortilla. Measure the diameter of (a) Will a sample obtained using Method 2 be representative of the population of all tortillas made that day, with respect to the diameters of the tortillas? Explain why or why not. No, bk only one production line is being used. Production Line B is centered above the advertised diameter of 6in, white Prod, Line A is centered below the advertised population, a sample of of 61n. To ine should STATISTICS FREE-RESPONSE QUESTIONS (b) The figure below is a histogram of 200 diameters obtained by using one of the methods described. Considering the shape of the histogram, explain which Method 2, was most likely used to obtain such a sample. There are peaks in this h one at 5.9 & the other at 6.1. If method 1 is used, values should be very close to 5.9 or 6.1, (centered) which they are. [Histogram Image] (c) Which of the two sampling methods, Method 1 result in less variability in the diameters of the 200 tortillas in the sample on a given day? sampling from one production line. If you sample from 2 lines, the variability Each day, the distribution of the 200,000 tortillas made that 6 inches with standard deviation 0.11 inch. (d) For samples of size 200 taken from one day's production, describe of the sample er fo les obtai sing M 1. pe is normally distributed. (e) Suppose that one of the two sampling methods will be selected and used every day for one year (365 days). The 1 sample mean of the 200 diameters will be recorded each day. Which of the two methods will result in less variability in the distribution of the 365 sample means? Explain 2   Method 2 blc one line has less variation than when 2 or more are used. (f) A government inspector visit the facility on June 22 to observe the sampling e if the is unsure which method is more to d d er of 6 inches. The manager knows that, with both a d ator of the population mean. However, the manager on your previous answers, w mean that is close to 6 inches on the of or 2, is oduce a sample mean close to 6 inches? Explain. Method 1 should have a mean close to 6 inches. If Method 2 is used, the mean will either be close to 5.9 in or 6.1 in. Since method 1 is for all tortillas, the mean should be closer to 6. STOP END OF EXAM