After a number of complaints about its directory assistance, a telephone company examined samples of calls to determine the frequency of wrong numbers given to callers. Each sample consisted of 110 calls. SAMPLE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number of errors 6 3 5 2 2 6 3 3 5 10 3 2 5 4 6 5 ________________________________________a. Determine 95 percent limits. (Do not round your intermediate calculations. Round your final answers to 3 decimal places.) UCL LCL ________________________________________b. Is the process stable (i.e., in control)? YesNoEach of the processes listed is noncentered with respect to the specifications for that process.Process Mean StandardDeviation LowerSpec UpperSpecH 18.7 .45 17.5 20.2K 32.2 1.01 29.8 35.0T 24.8 .38 23.2 26.9________________________________________Compute the appropriate capability index for each, and decide if the process is capable. (Round your answers to 2 decimal places.) Process Cpk Capable?H K T The time needed for checking in at a hotel is to be investigated. Historically, the process has had a standard deviation equal to .146. The means of 39 samples of n = 24 areSample Mean Sample Mean Sample Mean Sample Mean1 3.86 11 3.88 21 3.84 31 3.882 3.90 12 3.86 22 3.82 32 3.763 3.83 13 3.88 23 3.89 33 3.834 3.81 14 3.81 24 3.86 34 3.775 3.84 15 3.83 25 3.88 35 3.866 3.83 16 3.86 26 3.90 36 3.807 3.87 17 3.82 27 3.81 37 3.848 3.88 18 3.86 28 3.86 38 3.799 3.84 19 3.84 29 3.98 39 3.8510 3.80 20 3.87 30 3.96 ________________________________________a-1. Construct an -chart for this process with three-sigma limits. (Do not round intermediate calculations. Round your answers to 2 decimal places.) UCL LCL ________________________________________a-2. Is the process in control? YesNob. Analyze the data using a median run test and an up/down run test. What can you conclude?Test Conclusion Median Up/Down ________________________________________Using samples of 190 credit card statements, an auditor found the following:Use Table-A. Sample 1 2 3 4 Number with errors 4 2 6 8________________________________________ a. Determine the fraction defective in each sample. (Round your answers to 4 decimal places.) Sample Fraction defective1 2 3 4 ________________________________________ b. If the true fraction defective for this process is unknown, what is your estimate of it? (Round your answer to 1 decimal place. Omit the “%” sign in your response.) Estimate % c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? (Round your intermediate calculations and final answers to 4 decimal places.) Mean Standard deviation ________________________________________ d. What control limits would give an alpha risk of .03 for this process? (Round your intermediate calculations to 4 decimal places. Round your “z” value to 2 decimal places and other answers to 4 decimal places.) z = , to e. What alpha risk would control limits of .047 and .006 provide? (Round your intermediate calculations to 4 decimal places. Round your “z” value to 2 decimal places and “alpha risk” value to 4 decimal places.) z = , alpha risk = f. Using control limits of .047 and .006, is the process in control? yesno g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? (Round your intermediate calculations and final answers to 2 decimal places.) Mean Standard deviation ________________________________________ h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control? YesNo
