DaitrusGarnes_MTH140_Week5_CourseProject
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According to Prison Policy Initiative, with nearly two million people behind bars at any given time, the United States has the highest incarceration rate of any country in the world. We spend about $182 billion every year, not to mention the significant social cost, to lock up nearly 1% of our adult population. To be able to evaluate this policy choice, our communities must have
access to reliable and up-to-date information about the trajectory and scope of our nation’s experiment with mass incarceration (Wagner, 2023). Let’s look at the state imprisonment rates for the year of 2021 followed by imprisonment rates of 2021 dispersed by ethnicity and sex to project the layout of mass incarceration within the United States. What we hope to find from these data sets are the amounts of incarceration per 100,000 of the population per state and the correlation of incarcerated individuals based on sex and ethnicity throughout the United States for the year of 2021.
The Bureau of Justice Statistics keep collection records of the nation’s local, state,
private, and federal detention centers, jails and prisons. In 2021 data was collected through the Bureau of Justice Statistics regarding the state imprisonment rates (number of incarcerations per 100,000 people in the state) for the 50 states in the US. The graph below shows the incarceration
data for each state in the year of 2021 per 100,000 of the population.
The sample included incarcerated individuals within each state out of the entire state population.
(Statista Research Department, 2023-a).
From the graph above, we can determine that Mississippi had the highest number of incarcerated individuals while Massachusetts had the lowest. The mean of this data set can be calculated by adding up the values in the data set and then dividing by the number of values that you added. Therefore, adding up each incarcerated value for each state we get 15,018. Now, we divide by 50 to get the mean. The mean for this data set is 300.36 round to nearest whole number
is 300.
To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list. Let’s start with the lowest value and increase to the highest value: With an even number of values, there will be two middle numbers. These numbers
are 287 and 298. To get the median, we add these numbers together and divide by 2. Therefore, the median of this data set is 292.5.
The mode is the number in a data set that occurs most frequently. Looking at the graph, we can determine that the mode of the data set is 267. The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean. A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean. To calculate the standard deviation, the equation is as follows: whereas O = population standard deviation, N = the size of the population, Xi = each value from the population, and u = the population mean. The first step is to find the mean. The mean is 300 from
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earlier calculation. Next step is to find each value’s deviation from the mean. These new values are -204, -193, -182, -166, -165, -160, -148, -146, -145, -125, -124, -119, -87, -85, -75, -60, -55, -41, -33, -33, -29, -24, -20, -14, -13, -2, 10, 14, 18, 20, 23, 28, 35, 51, 66, 67, 71, 74, 82, 84, 87, 111, 127, 143, 149, 153, 255, 259, 264, 275.
The next step in calculating the standard deviation of the data set is squaring all the deviation values. The new values are now 41,616; 37,249; 33,124; 27,556; 27,225; 25,600; 21,904; 21,316; 21,025; 15,625; 15,376; 14,161; 7,569; 7,225; 5,625; 3,600; 3,025; 1,681; 1,089;
1,089; 841; 576; 400; 196; 169; 4; 100; 196; 324; 400; 529; 784; 1,225; 2,601; 4,356; 4,489; 5,041; 5,476; 6,724; 7,056; 7,569; 12,321; 16,129; 20,449; 22,201; 23,409; 65,025; 67,081; 69,696; 75,625.
The next step is summing all the square values. The sum of all the square values in this data set is 753,672. After calculating the sum, you find the variance by dividing the sum of the squares by n – 1 (for a sample) or N (for a population) – this is the variance. Therefore, the variance calculation is 75,625 / (50-1), which equals 75,625 / 49, which equals 1,543 rounded to nearest whole number. Next step is to find the square root of the variance. The square root of 1,543 is 39.28. This is the standard deviation, 39.28. Therefore, we can say each value deviates from the mean by 39.28 on average within this data set.
The Bureau of Justice Statistics keep collection records of the nation’s local, state, private, and federal detention centers, jails and prisons. In 2021 data was collected through the Bureau of Justice Statistics regarding the imprisonment rate of sentenced prisoners in the United
States under federal or state jurisdiction in 2021, by sex and ethnicity (per 100,000 residents). The graph below shows the incarceration data for each race and sex in the year of 2021 per 100,000 of the residents. The sample included incarcerated individuals within the United States. The overall imprisonment rate in 2021 stood at 350 per 100,000 Americans.
(Statista Research Department, 2023-b).
According to the data from the graph, the greatest ethnicity to have been incarcerated in 2021 was Other for both male and female, while the least was Asian for both male and female. From this data set, we can conclude that in the year 2021, the majority of incarcerated individuals based on sex were male and the majority of incarcerated individuals based on ethnicity were other (two or more ethnicities, and ethnicities not noted). Therefore, if an even presumption is presumed over the board, in correlation, each state would have more incarcerated individuals who classify as other and less incarcerated individuals who classify as Asian. Analyzing and
calculating these data sets can help law enforcement and government officials tackle speculative narratives such as African Americans being incarcerated at a substantial higher rate than other ethnicities.
As for my hypothesis, I speculate that mean incarceration rate of state prisoners within the U.S. is at least 336 per 100,000 residents. A random sample of 15,018 per 100,000 residents has a mean of 300 per 100,000 residents. With the assumption that the population is normally distributed, and the population standard deviation is 39.28 per 100,000 residents, at a = 0.05, is there enough evidence to reject my claim?
First, we need to identify the null hypothesis and alternative hypothesis. To find the null and alternative hypotheses, start by writing the claim mathematically. Express the claim, "mean incarceration rate of state prisoners within the U.S. at a certain rate," mathematically:
u >
336
The other hypothesis is the complement of the claim. Therefore, the compliment is:
u < 336
Ho u >
336
Ha u < 336
Next, Identify the critical values. Find the z-score that depends on the hypothesis test. Since the hypothesis test is left-tailed, the critical value is the z-score corresponding to an area of a:
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a = 0.05; Using the Z-Score Table, we can successfully find the z-score corresponding to the area
equal to 0.05 to the left of Zo.
Therefore, Zo is approximately -1.64:
Zo = -1.64
Next, we identify the standardized test statistic. The standardized test statistic z is given by the formula: Z = (x
– u) / (o/sqrt <n>) where u is the population mean, x
is the sample mean, o is equal to the standard deviation, and n is the sample size. Therefore, the equation is:
Z = (300 – 336) / (39.28 / sqrt <15,018>)
Z = (-36) / (39.28 / 122.548)
Z = (-36) / 0.321)
Z = -112.15
Now, we decide whether to reject or fail to reject the null hypothesis. To determine whether to reject or fail to reject the null hypothesis, compare the standardized test statistic z to the rejection
region z < -1.64. The standardized test statistic z = -112.15 is in the rejection region. Therefore, we can reject Ho because there is sufficient evidence to reject the claim that mean state incarceration rates within the U.S. is at least 336 per 100,000 residents.
REFERENCES
Wagner, P. (2023, March 14). Prison Policy Initiative. United States Profile. Retrieved from: https://www.prisonpolicy.org/profiles/US.html
Statista Research Department. (2023-a, June 02). Statista. Imprisonment Rate of State Prisoners in the United States in 2021, By State. Retrieved from: https://libproxy.ecpi.edu:2084/statistics/302411/state-prisoner-imprisonment-rate-us/
Statista Research Department. (2023-b, June 02). Statista. Imprisonment Rates of Sentenced Prisoners in the United States Under Federal or State Jurisdiction in 2021, By Sex and Ethnicity.
Retrieved from: https://www.statista.com/statistics/252871/imprisonment-rate-of-sentenced-
prisoners-in-the-us-by-sex-and-ethnicity/
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