Statistics Assignment

I consider data sets namely number of violent crimes, number of property crimes, violent crime rates, and property crime rates for the years 1960 through 2012 for my analysis. Violent crime have has 4 categories Murder and non-negligent Manslaughter, Legacy rape /1, Robbery and Aggravated assault. Property crimes has 3 categories Burglary, Larceny-theft and Motor vehicle theft.

The table of descriptive statistics for total of violent crimes, total of property crimes, violent crime rates, and property crime rates along with population is given below.

There are 53 observation for each year from 1960 to 2012. All the variables total of violent crimes, total of property crimes, violent crime rates, and property crime rates are observed to be skewed to the left. For a skewed data, median is considered as the best measure of central tendency. Median is the middle observation in a series of data when arranged in ascending order. The value of median for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 2744, 54573, 247.6, and 5143.3 respectively.

Mean is defined as the sum of all observation divided by total number of observations. The mean value for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 2332.321, 51414.22, 213.07 and 4940.67 respectively. The value of standard deviation and variance is a measure of dispersion around mean. The value of standard deviation for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 1108.06, 17155.94, 82 and 1306.65. The low value of standard deviation of Violent Crime rate and Property crime rate implies that its mean is reliable. But high value of standard deviation of total of violent crimes and total of property crimes implies that mean is not reliable.

The descriptive statistics for 4 categories of violent crime namely Murder and non-negligent Manslaughter, Legacy rape /1, Robbery and Aggravated assault is given below.

Legacy rape /1 and Robbery are skewed to the left. Category Murder and non-negligent Manslaughter and Aggravated assault is skewed to the right. For a skewed data median is the best measure of central tendency. Median for Murder and non-negligent Manslaughter, Legacy rape /1, Robbery and Aggravated assault is 35, 333, 1065 and 1095 respectively.

The descriptive statistics for 4 categories of violent crime rate namely Murder and non-negligent Manslaughter rate, Legacy rape /1 rate, Robbery rate and Aggravated assault rate is given below.

Legacy rape rate /1, Robbery rate and Aggravated assault rate are skewed to the left. Murder and non-negligent manslaughter rate is observed to be skewed to right. Median for Murder and non-negligent Manslaughter rate, Legacy rape /1 rate, Robbery rate and Aggravated assault rate is 3.4, 28.2, 91.4 and 112.7 respectively.

The descriptive statistics for 3 categories of Property crime namely Burglary, Larceny-theft and Motor vehicle theft is given below.

Burglary, Larceny-theft and Motor vehicle theft is skewed to the right. For a skewed data, median is the best measure of central tendency. Median for Burglary, Larceny-theft and Motor vehicle theft is11409, 38329 and 4469.

The descriptive statistics for Burglary rate, Larceny-theft rate and Motor vehicle theft rate is given below.

Burglary rate and Motor vehicle theft rate is skewed to the right. Larceny-theft rate is skewed to the left. For a skewed data, median is the best measure of central tendency. Median for Burglary rate, Larceny-theft rate and Motor vehicle theft rate is 1152.4, 3544.3 and 430.1 respectively.

The histogram violent crime rates (as well as its categories) for the years 1960 through 2012 is given below.

Legacy rape rate /1, Robbery rate and Aggravated assault rate are skewed to the left. Murder and non-negligent manslaughter rate is observed to be skewed to right. This implies there are very few years with low Legacy rape rate /1, Robbery rate and Aggravated assault rate. Also, there are very few years with high Murder and non-negligent manslaughter rate.

The histogram property crime rates (as well as its categories) for the years 1960 through 2012 is given below.

Burglary rate and Motor vehicle theft rate is skewed to the right. Larceny-theft rate is skewed to the left. This implies there are very few years with high Burglary rate and Motor vehicle theft rate. Also, there are very few years with low Larceny-theft rate.

The boxplot for total property crimes (as well as its categories) for the years 1960 through 2012 is given below. I observe that there are no outliers in the data.

The boxplot for total violent crimes (as well as its categories) for the years 1960 through 2012 is given below. I observe that there are no outliers in the data.

The scatterplot for namely number of violent crimes, number of property crimes, violent crime rates, and property crime rates for the years 1960 through 2012 is given below.

There is strong positive linear relationship observed between violent crime total and year as well as violent crime rate and year. That with every year, the value of total violent crime increases. With increase in every year, the value of violent crime rate also increases.

There is a moderate positive linear relationship observed between property crime total and year as well as property crime rate and year. That with every year, the value of total property crime increases. With increase in every year, the value of property crime rate also increases.

The 95% confidence interval for the mean murder and non-negligent manslaughter rate is calculated with the help of following formula.

The 95% confidence interval for the mean murder is (33.2, 42.34). Calculations are shown below.

I am 95% confident that estimated population mean for mean murder lies in the interval (33.2, 42.34).

The 95% confidence interval for the mean non-negligent manslaughter rate is (3.30, 4.31). Calculations are shown below.

I am 95% confident that estimated population mean for mean non-negligent manslaughter rate lies in the interval (3.30, 4.31).

I want to test if mean property crime rates for 1960 through 1981 (collectively) are different from the mean property crime rates from 1982 through 2012. The two variables for years 1960 through 1981 and 1982 through 2012 are dependent on each other. Hence I apply paired t test.

Consider null hypothesis, ho: there is no significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012. This is tested against the alternative hypothesis, h1; there is significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012.

With t = -7.29 and p-value < 0.05 (alpha), I reject null hypothesis and conclude that there is significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012.

It is important to check for assumption of normality for application of parametric test. Shapiro-Wilk test and Kolmogorov-Smirnov (K-S) are few test to check the assumption of normality. A bell shaped histogram is said to have normal distribution. A PP plot with S shape is also said to follow normal distribution.

It is also required to check that all units are measured in same units. If it is not true then raw data should be converted into z scores.

· The variables total of violent crimes, total of property crimes, violent crime rates, and property crime rates are observed to be skewed to the left.

· The value of median for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 2744, 54573, 247.6, and 5143.3 respectively.

· Legacy rape /1 and Robbery are skewed to the left. Category Murder and non-negligent Manslaughter and Aggravated assault is skewed to the right.

· Legacy rape rate /1, Robbery rate and Aggravated assault rate are skewed to the left. Murder and non-negligent manslaughter rate is observed to be skewed to right.

· Burglary, Larceny-theft and Motor vehicle theft is skewed to the right.

· Burglary rate and Motor vehicle theft rate is skewed to the right. Larceny-theft rate is skewed to the left.

· There are no outliers in the data.

· There is strong positive linear relationship observed between violent crime total and year.

· There is a moderate positive linear relationship observed between property crime total and year

· I am 95% confident that estimated population mean for mean murder lies in the interval (33.2, 42.34).

· I am 95% confident that estimated population mean for mean non-negligent manslaughter rate lies in the interval (3.30, 4.31).

· There is significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012.

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Histogram of Population, Violent Crim, Murder and n, Legacy rape , ...

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Histogram of Population, Property cri, Burglary rat, Larceny-thef, ...

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