PART 1:
“Hours in Cells” exercise
The Department of Justice reports in 2004 that its researchers have surveyed all the correctional facilities in the United States and that the average number of hours a prisoner spends locked in a cell is 15 hours a day. This is the “population mean.” The Justice Department also tells us that the standard deviation is 4 hours, considering all the facilities.
But a group of penologists from a respected university suspect that the increased use of isolation as a tactic to control prisoners has increased the time prisoners spend in their cells. To investigate this hypothesis (that prisoners in 2007 are spending more time in their cells than in was reported in 2004), these independent researchers made a list of all correctional facilities and selected 30 at random. They then went to these facilities and, using the records of the individual facilities, recorded the average time a prisoner was confined to a cell.
The data collected for each facility is in the “Hours in the Cell” excel file in your Data-based Assignment folder. NOTE: I would recommend using EXCEL to make all calculations.
Section 1:
a. Calculate the sample mean, the average number of hours in a cell per day from the 30 correctional facilities studied by the researchers.
b. Calculate the standard deviation of the sample mean.
c. On average, are inmates in 2007 spending more time in their cells than in 2004? What is the difference between the two means?
d. What is the “hours in the cell” range for “middle 68%” of the distribution in 2007 and 2004? Which of the two distributions has more variability around the mean?
e. In 2004, if you selected a correctional facility at random. What is the probability that inmates in that correctional facility would spend on average more 19 hours in their cells?
Answer the same question for the sample selected in 2007.
PART 2:
For this part of the assignment, you will be asked to work with the dataset “NELS Dataset.” This is a dataset that contains information from student surveys and tests and from surveys of parents, school administrators, and teachers. It was designed to provide trend data about critical transitions experienced by students as they leave elementary school and progress through high school and postsecondary institutions or the work force. Make sure to answer each question in a thoughtful, well-written manner.
Section 1: Subjects and Variables
a. What is the sample size? That is, how many respondents are in this dataset?
b. How many variables are in this dataset?
c. For the variables Homelang, schtyp8, hwkin12, and apoffer, tell me: What is the label for this variable? What values are assigned to each number? What is the level of measurement? (NOTE: if variable is interval/ratio omit the second question).
d. The respondents that did not answer the question for variable Expinc30 are called missing. What values did these missing respondents get? How many missing respondents were there?
Section 2: Organizing Data
a. Let’s take a look at the highest level of education expected (variable: edexoect). Do a frequency distribution of this variable. Paste table below.
b. How many of the respondents expect to get a PhD., MD, or JD?
c. What percentage of respondents expect to get a Bachelor’s degree or lower?
d. If two respondents were selected randomly from this dataset, what is the probability that both respondents expect Bachelor’s degree?
e. Choose an appropriate method to graph this variable. Paste below.
f. It would be interesting to see if the highest level of education expected is influenced by gender. Theoretically speaking, how could gender influence highest level of education expected? That is, do you expect to see differences between men and women in the expected highest level of education? Why or why not?
g. Do a crosstabulation of edexoect and gender. Be mindful of which variable you place in the column and row. Also make sure the table has “column percentage.” Paste below.
h. What is the probability that, given that you are a female, you expect a PhD., MD, or JD? Given that you are a male, what is the probability that you expect to get a Bachelor’s degree?
i. Based, on the crosstabulation. Does gender seem to influence the respondent’s level of education expected? Why or why not?
j. Do another cross tabulation between gender and alcbinge. Paste the table. Does gender seem to have an influence on whether the respondents binge drinks or not? Why or why not?
Section 3: Recoding Variables:
a. Do a frequency Distribution of absent12 that is, the number of times a student missed school in the 12th Grade? Paste below.
b. From a researcher’s perspective, those respondents that miss 7-9 times, 10-15 times and over 15 times, might not very different from each other. Thus, it would OK to lump them together. Use the recode function in SPSS to recode absent12 in three categories. 1 = never, 2= 1-2 times, 3= 3-6 times, and 4= over 7 times. Paste a frequency distribution of the recoded variable.
Section 4: Measures of Central Tendency and Dispersion
a. Let’s take a look at the expected income at age 30 (expinc30). Report the Mean, Median and Mode. What do the mean, mean and mode tell you about the shape of the distribution? Which measure of central tendency is appropriate for this distribution?
b. Use the most appropriate graph to illustrate the shape of the distribution and fit a normal curve as well. Paste below
c. Report the range, maximum value, minimum value, variance, Interquartile range, and standard deviation expinc30. Which of these would you use as a measure of dispersion?
d. Do question a,b, and c, but for variable achsci12—science achievement in the 12th grade.
e. Is the distribution roughly normal? Why or why not?
f. Assuming that the distribution is completely normal, what grade do you need to get to be 2 standards deviation away above the mean? What proportion of students scored below this grade?