1). Explain the difference between the information given by the tests of statistical significance t and Chi Square, and measures of association Cramer's V, Gamma and Pearson's correlation coefficient, r.
Can a test of significance show a statistically significant relationship while a measure of association shows a weak relationship between the variables?
If yes, present an example illustrating how such a situation might occur.
2).
Flip a coin 60 times. Record the outcome of each of the 60 flips in order from 1 to 60, using the Tally Sheet accompanying the Final Exam. Tally the number of heads and the number of tails and calculate the proportion of heads in your sample.
Based on your sample result, calculate a 95% Confidence Interval for the true population value. Calculate a 95% Confidence Interval for the proportion of heads.
3). To locate treatment programs for heroin addicts, the mayor wants to conduct a study of persons arrested for possession in your city.
He suggests looking at data on location of arrest and residence of arrestees for the past month. This will yield a sample of at least eighty cases. From his statistics course, he says that with a sample size greater than 50, the central limit theorem will apply and you can to make a reasonable estimate of the numbers of people needing treatment with a level of confidence of 95%.
Is the mayor correct? From your knowledge of criminal justice and statistical analysis would you suggest a different sampling plan? If yes, what would you suggest?
4)
ou hypothesize that there is a relationship between an individual's level of Self Control as measured by the Grasmick Self Control Scale (Self_Con) and his or her Number of Adult Arrests (ARR). Theory postulates that low self control is associated with higher number of arrests. Use the definitions of the variables contained in the Week One Dataset, reprinted below.
State your null and research hypotheses.
Variables are defined as follows: SELF_CON Grasmick Self-Control Scale Treated as interval-ratio level. A scale measuring self-control developed by Richard Grasmick. Scores may range from 24 to 96, with low scores indicating low self-control. 99 = No data in Record
ARR Number of adult arrests as recorded in court records. An interval-ratio level variable. Since all members of the population have (by definition) been arrested at least once, values will range from 1 to nn 99 = No data
Explain the following results from the SPSS output that can be found in this linked file called "Regression Data":
1. Mean and standard deviation for each variable.
2. The interpretation of the Pearson Correlation
3. R square
4. Unstandardized coefficients : (Constant and Self_Con)
5. Calculate the number of arrests for a person with a Self-Con score of 50.
5).
A researcher conducts a study of white and black attitudes toward the police in her community.
The percentage of a random sample of white respondents (N = 250) who say they have a favorable attitude toward the police is 55%. The percentage of a random sample of black respondents (N = 300) who say they have a favorable attitude toward the police is 41%.
You are asked if there is a real difference between the percentage of whites and blacks who have a positive attitude toward the police in the larger population, or is this sample difference likely to have occurred by random chance or sampling error.
How do you respond? Explain your answer.
Construct a 95% confidence interval for the proportion of Whites in the population who have a favorable attitude toward the police.