Question

please solve for part A in second picture

Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The lizens 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 fighting 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 5.100 residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 1,020 of the 5,100 residences for data on crime. (Respondents are guaranteed anonymity) The 1,020 sampled from each area showed the following incidence of crime during the past month: AREA 1 2. 3 4 9 10 11 12 13 14 15 16 17 18 19 20 NUMBER OF CRIMES 12 1 17 16 12 24 12 15 10 2 16 13 10 12 8 24 3 16 5 24 252 SAMPLE SIZE CRIME RATE 1.020 0.012 1.020 0001 1.020 0.017 1,020 0.016 1,020 0.012 1.020 0.024 1.020 0.012 1020 0.015 1.020 0.010 1,020 0.002 1,020 0.010 1.020 0.013 1,020 0.010 1.020 0.012 1.020 0.000 1,020 0.024 1,020 0.003 1.020 0.010 1020 0.005 1,020

Answer 1

Total number of crimes = 252

Total sample size = number of samples*sample size = 1020*20 = 20400

p-bar = total number of crimes/total sample size = 252/20400 = 0.012353

p-bar = 0.0124 (rounded to four decimals)

UCL = p-bar + z*√(p-bar*(1 – p-bar)/n)

Here,

p-bar = 0.0124

z = 1.96

n = 1020

UCL = 0.0124 + 1.96*√(0.0124 * 0.9876 / 1020)

= 0.0191

UCL = 0.0191

LCL = p-bar – z*√(p-bar*(1 – p-bar)/n)

= 0.0124 – 1.96*√(0.0124 * 0.9876 / 1020)

= 0.0056

LCL = 0.0056

***Please define what Sp is in comment. There are different formulae for Sp and your answer might get wrong. I will update the answer accordingly.

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