The state and local police departments are trying to analyze crime rates so they

Question

The state and local police departments are trying to analyze crime rates so they can shift their patrols from decreasing-rate areas to areas where rates are increasing. The city and county have been geographically segmented into areas containing 4,500 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 900 of the 4,500 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area:

b. If the next three months show crime incidences in this area as

January = 10 (out of 900 sampled)

February = 12 (out of 900 sampled)

March = 11 (out of 900 sampled)

What comments can you make regarding the crime rate?

MONTH CRIME INCIDENCE SAMPLE SIZE CRIME RATE January 10 900 0 February 12 900 0 March 10 900 0 April 10 900 0 May 10 900 0 June 12 900 0 July 10 900 0 August 13 900 0 September 11 900 0 October 14 900 0 November 12 900 0 December 9 900 0

Explanation / Answer

Answer to question a :

Total number of crime incidence

= 10 + 12 + 10 + 10 + 10 + 12 + 10 + 13 + 11 + 14 + 12 + 9

= 133

Total number of residence contacted

= 900 /month x 12 months

= 10800

Thus sample size = n = 900

Therefore , proportion of crime rate = Pbar =   133 / 10800 = 0.0123

Standard deviation = Sp

= Square root ( Pbar x ( 1 – Pbar)/ n)

= ( 0.0123 x 0.9877 / 900)

= 0.00367

Upper control limit at Z = 1.96 will be

= UCL = Pbar + 1.96 x Sp = 0.0123 + 1.96 x 0.00367 = 0.0123 + 0.00719 = 0.01949

Lower Control Limit at Z = 1.96 will be

= LCL = Pbar + 1.96 x Sp = 0.0123 - 1.96 x 0.00367 = 0.0123 - 0.00719 = 0.00511

Pbar

0.0123

Sp

0.00357

UCL

0.019490

LCL

0.00511

Answer to question b :

The proportion of crime incidence for three months are :

January = 10/900 = 0.01111

February = 12/ 900 = 0.01333

March = 11/ 900 = 0.01222

These numbers are within control limit range 0.00511 and 0.019490 .Therefore we can say that the crime rates are within control limits

Pbar

0.0123

Sp

0.00357

UCL

0.019490

LCL

0.00511

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