Some citizens complained to city council members that there should be equal prot

Question

Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. The city has been broken down into 20 geographic areas, each containing 5,000 residences. The 1,070 sampled from each area showed the following incidence of crime during the past month:

AREA NUMBER OF CRIMES SAMPLE SIZE CRIME RATE 1    17         1,070         0.016        2    6         1,070         0.006        3    22         1,070         0.021        4    21         1,070         0.020        5    17         1,070         0.016        6    34         1,070         0.032        7    13         1,070         0.012        8    22         1,070         0.021        9    15         1,070         0.014        10    4         1,070         0.004        11    26         1,070         0.024        12    18         1,070         0.017        13    15         1,070         0.014        14    17         1,070         0.016        15    13         1,070         0.012        16    39         1,070         0.036        17    5         1,070         0.005        18    26         1,070         0.024        19    7         1,070         0.007        20    39         1,070         0.036        376        

a. Determine , Sp, UCL and LCL for a p chart of 95 percent confidence (at Z = 1.96). (Round your answers to 5 decimal places.)      Sp   UCL   LCL

Explanation / Answer

Ans-

. Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1000 ohms each. To set up the machine and to create a control chart to be used throughout the run, 10 samples were taken with 4 resistors in each sample. The complete list of samples and their measured values are as follows: Sample No Readings in ohms 1 1010 991 985 986 2 995 996 1009 994 3 1015 1020 1009 998 4 1013 1019 1005 993 5 994 1001 994 1005 6 990 1003 1015 1008 7 1001 986 996 996 8 996 1006 997 989 9 981 991 989 1003 10 999 993 988 984 i. Is this process in control? ANS (i) S.No Mean X R 1 1010 991 985 986 993.0 25 2 995 996 1009 994 998.5 15 3 1015 1020 1009 998 1010.5 22 4 1013 1019 1005 993 1007.5 26 5 994 1001 994 1005 998.5 11 6 990 1003 1015 1008 1004.0 25 7 1001 986 996 996 994.8 15 8 996 1006 997 989 997.0 17 9 981 991 989 1003 991.0 22 10 999 993 988 984 991.0 15 9985.8 193 Readings in ohms X = 9985.8/10 = 998.6 ohms R = 193/10 = 19.3 ohms UCLX = X + A2R LCLX = X – A2R UCLR = D4R LCLR = D3R From the table A2 = 0.73 D4 = 2.28 D3 = 0 UCLX = 998.6 + 0.73*19.3 = 1012.7 ohms LCLX = 998.6 - 0.73*19.3 = 984.5 ohms UCLR = 2.28*19.3 = 44 ohms LCLR = 0 Charles Lackey, the owner, does not believe things have changed much, but he did invest an additional $3,000 for modifications to the bakery’s ovens to make them more energy-efficient. The modifications were supposed to make the ovens at least 15% more efficient, but extra labor-hours were required for workers to become familiar with the process changes. Lackey has asked you to check the energy savings of the new ovens and also look over other measures of the bakery’s productivity to see if the modifications were beneficial. He has the following data representing a month from last year and an equivalent month this year:: Last year Now Production (dozen) 1,500 1,500 Labor (hours) 350 325 Capital Invested ($) $15,000 $18,000 Energy (BTU) 3,000 2,750 Determine the multifactor productivity using the following costs: - labor $8 per hour - capital 0.83% per month of investment - energy $0.60 per BTU You are to provide Mr Lackey with a multifactor indication of the productivity increase or decrease between last year and this year. Energy Change: Last year : 1500*12/3000 = 6.0 loaves/BTU Now : 1500*12/2750 = 6.55 loaves/BTU Percent Change: (6.55-6)/6*100= 9.17% There has definitely been an increase in the energy productivity which means there have been savings in energy. Labor Change: Last year : 1500*12/350 = 51.43 loaves/labor hour Now : 1500*12/325 = 55.38 loaves/labor hour Percent Change: (55.38-51.43)/51.43*100= 7.68% There is also an increase in labor productivity Investment Change: Last year : 1500*12/15000 = 1.2 loaves/$ investment Now : 1500*12/18000 = 1.0 loaves/$ investment Percent Change: (1.0-1.2)/1.2*100= -16.67% However as we can see there has been a decrease in the investment productivity. This can be however be substantiated with the fact that due to this investment, the energy savings is now possible and that this has cause an increase in the energy productivity. Now looking at the total multifactor productivity figures Last year : 1500*12/(350*8+3000*0.6+15000*.0083) = 3.81 Now : 1500*12/(325*8+2750*0.6+18000*.0083) = 4.09 Percent Change: (4.09-3.81)/3.81*100= 7.35% So as can be seen the modification could only make the ovens 7.35% more efficient and not 15% more efficient.

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