Answered: Death row and the single-sample t test:…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Death row and the single-sample t test: The Florida Department of Corrections publishes an online death row fact sheet. It reports the average time on death row fact sheet. It reports the average time on death row prior to execution as 11.72 years provides no standard deviation. This mean is a parameter because it is calculated from the entire population of executed prisoners in Florida. Did the time spent on death row change over time? According to the execution list linked to the same Web site, the six prisoners executed in Florida during the 2003,2004, and 2005 spent 25.62, 13.09, 8.74, 17.63, 2.80, and 4.42 years on death row, respectively. (All were men, although Aileen Wuornos, the serial killer portrayed by Charlize Theron in the 2003 film Monster, was among the three prisoners executed by the state of Florida in 2002; Wuornos spent 10.69 years on death row.)

a. Using symbolic notation and formulas (where appropriate), determine the appropriate mean and standard error for the distribution of means. Show all your steps of your calculations.

b. Using symbolic notation and the formula, calculate the t statistic for time spent on death row for the sample of executed prisoners.

c. The execution list provides data on all prisoners executed since the death penalty was reinstated in Florida in 1976. Included for each prisoner are the name, race. Gender, date of birth, date of offense, date sentenced, date arrived on death row, data of execution, number of warrants, and years on death row. State atleast one hypothesis, other, other than year of execution, which could be examined using a t distribution and the comparison mean of 11.72 years on death row. Be specific about your hypothesis (and if you are interested, you can search for the data online).

d. What additional information would you need to calculate a z score for the length of time Aileen Wuornos spent on death row?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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