Essentials Of Statistics
Essentials Of Statistics
4th Edition
ISBN: 9781305093836
Author: HEALEY, Joseph F.
Publisher: Cengage Learning,
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Chapter 2, Problem 2.4P

CJ The numbers of homicides in five U.S. states and five Canadian provinces for the years 1997 and 2012 are presented in two accompanying tables.

a. Calculate the homicide rate per 100,000 populations for each state and each province for each year. Relatively speaking, which state and which province had the highest homicide rates in each year? Which society seems to have the higher homicide rate? Write a paragraph describing these results?

b. Using the rates you calculated in part a, calculate the percent change between 1997 and 2012 for each state and each province. Which states and provinces had the largest increase and decrease? Which society seems to have the largest change in homicide rates? Summarize your results in a paragraph.

State 1997 2012
Homicides Population Homicides Population
New Jersey 338 8,053,000 388 8,864,590
Iowa 52 2,852,000 45 3,074,186
Alabama 426 4,139,000 342 4,882,023
Texas 1327 19,439,000 1144 26,059,203
California 2579 32,268,000 1884 38,041,430

Source: Federal Bureau of Investigation. Uniform Crime Reports. Retrieved from http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2012/crime-in-the-u.s.-2012/tables/4tabledatadecoverviewpdf/table_4_crime_in_the_united_states_by_region_geographic_division_and_state_2011-2012.xls

Province 1997 2012
Homicides Population Homicides Population
Nova Scotia 24 936,100 17 945,100
Quebec 132 7,323,600 108 8,043,600
Ontario 178 11,387,400 162 13,490,500
Manitoba 31 1,137,900 52 1,274,100
British Columbia 116 3,997,100 71 4,678,100

Source: Statistics Canada. Retrieved from http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/legal12a-eng.htm

Expert Solution
Check Mark
To determine

a)

To calculate:

The homicide rate per 100, 000 populations for each state and each province for each year.

Answer to Problem 2.4P

Solution:

The homicide rates per 100, 000 populations for each state and each province for each year are:

State 1997 2012
Rate Homicides
New Jersey 3388,053,000*100,000= 4.20 3888,864,590*100,000= 4.38
Iowa 522,852,000*100,000= 1.82 453,074,186*100,000= 1.46
Alabama 4264,139,000*100,000= 10.29 3424,882,023*100,000= 7.01
Texas 132719,439,000*100,000= 6.83 114426,059,203*100,000= 4.39
California 257932,268,000*100,000=7.99 188438,041,430*100,000= 4.95

In the year 1997, the state Alabama has the highest homicide rate of 10.29 compare to other states. In the year 2012, the state California has the highest homicide rate of 4.95 compare to other states.

Province 1997 2012
Homicides Homicides
Nova Scotia 24936,100*100,000= 2.56 17945,100*100,000= 1.80
Quebec 1327,323,600*100,000= 1.80 1088,043,600*100,000= 1.34
Ontario 17811,387,400*100,000 = 1.56 16213,490,500*100,000 = 1.20
Manitoba 311,137,900*100,000= 2.72 521,274,100*100,000 = 4.08
British Columbia 1163,997,100*100,000= 2.90 714,678,100*100,000= 1.52

In the year 1997, the Province British Columbia has the highest homicide rate of 2.90 compare to other Provinces. In the year 2012, the Province Manitoba has the highest homicide rate of 4.08 compare to other provinces.

By comparing the homicide rates of the states and provinces of the year 1997, the homicide rate is higher for states; however, by comparing the homicide rates of the states and provinces of the year 2012, the homicide rate is higher for Provinces.

Explanation of Solution

Formula Used:

Rate = Actual OccurrenceTotal number of possible occurrence*Some unit

For State:

For rate per 100, 000, substitute Actual occurrence = 338, and Total number of possible occurrence = 8, 053, 000, therefore, rate of Homicides in the state New Jersey is:

Rate = 3388,053,000*100,000= 4.20.

Continuing in the similar way for other states, we have,

State 1997 2012
Rate Homicides
New Jersey 3388,053,000*100,000= 4.20 3888,864,590*100,000= 4.38
Iowa 522,852,000*100,000= 1.82 453,074,186*100,000= 1.46
Alabama 4264,139,000*100,000= 10.29 3424,882,023*100,000= 7.01
Texas 132719,439,000*100,000= 6.83 114426,059,203*100,000= 4.39
California 257932,268,000*100,000=7.99 188438,041,430*100,000= 4.95

For Province:

For rate per 100, 000, substitute Actual occurrence = 24, and Total number of possible occurrence = 936, 100, therefore, rate of Homicides in the Province Nova Scotia is:

Rate = 24936,100*100,000= 2.56

Continuing in the similar way for other Provinces, we have,

Province 1997 2012
Homicides Homicides
Nova Scotia 24936,100*100,000= 2.56 17945,100*100,000= 1.80
Quebec 1327,323,600*100,000= 1.80 1088,043,600*100,000= 1.34
Ontario 17811,387,400*100,000 = 1.56 16213,490,500*100,000 = 1.20
Manitoba 311,137,900*100,000= 2.72 521,274,100*100,000 = 4.08
British Columbia 1163,997,100*100,000= 2.90 714,678,100*100,000= 1.52

In the year 1997, the state Alabama has the highest homicide rate of 10.29 compare to other states. In the year 2012, the state California has the highest homicide rate of 4.95 compare to other states.

In the year 1997, the Province British Columbia has the highest homicide rate of 2.90 compare to other Provinces. In the year 2012, the Province Manitoba has the highest homicide rate of 4.08 compare to other provinces.

By comparing the homicide rates of the states and provinces of the year 1997, the homicide rate is higher for states; however, by comparing the homicide rates of the states and provinces of the year 2012, the homicide rate is higher for Provinces.

Expert Solution
Check Mark
To determine

b)

To calculate:

The percentage change between 1997 and 2012 for each state and province

Answer to Problem 2.4P

Solution:

State Percent Change
New Jersey 4.384.204.20*100= 4.28
Iowa 1.461.821.82*100= -19.72
Alabama 7.0110.2910.29*100= -31.94
Texas 4.396.836.83*100= -35.69
California 4.957.997.99*100= -38.04
State Percent Change
Nova Scotia 1.802.562.56*100= -29.84
Quebec 1.341.801.80*100= -25.51
Ontario 1.201.561.56*100= -23.18
Manitoba 4.082.722.72*100= 49.81
British Columbia 1.522.902.90*100= -47.70

The state New Jersey has the largest increase and the state California has the largest decrease in the rate. The province Manitoba has the largest increase and the province British Columbia has the largest decrease.

Explanation of Solution

Formula Used:

The formula of percent change is: f2f1f1*100.

Here, f1 is the value of the past year.

f2 is the value of the current year.

Now, for the state New Jersey,

f1 = 4.20.

f2 = 4.38.

The percent change is 4.384.204.20*100= 4.28.

Continuing in the same way for other states, we have,

State Percent Change
New Jersey 4.384.204.20*100= 4.28
Iowa 1.461.821.82*100= -19.72
Alabama 7.0110.2910.29*100= -31.94
Texas 4.396.836.83*100= -35.69
California 4.957.997.99*100= -38.04

Now, for the province Nova Scotia,

f1 = 2.56.

f2 = 1.80.

The percent change is 1.802.562.56*100= -29.84.

Continuing in the same way for other states, we have,

State Percent Change
Nova Scotia 1.802.562.56*100= -29.84
Quebec 1.341.801.80*100= -25.51
Ontario 1.201.561.56*100= -23.18
Manitoba 4.082.722.72*100= 49.81
British Columbia 1.522.902.90*100= -47.70

The state New Jersey has the largest increase and the state California has the largest decrease in the rate. The province Manitoba has the largest increase and the province British Columbia has the largest decrease.

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