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 Testing a Relationship between Pornography and Rape
Statistical Topic:
Researchers are often interested in determining a relationship between two variables not only for prediction but for determining possible causality.  Testing the correlation coefficient equal to 0 is the same as stating that no linear relationship exists between two variables.  Sample data analysis consist of drawing a scatterplot, computing a least squares linear regression line predicting y given x and computing r and r2. Both confidence intervals and hypothesis testing can determine if a linear relationship exists.  No regression equation can determine causality by other forms of scientific verification, added to the results of the inferential test, have to be used to determine causation. 
Student Issue:
The feminist view of rape is that violence against women, both sexual and nonsexual violence, is an expression of a male dominant social system.  Thus rape is construed as integral to the historic powerlessness of women in male-dominated societies.  Some researchers content that the proliferation of pornography is linked to rape and other violent crimes against women. 
Data Sets: 
Twenty states were randomly selected and the number of Playboys per 100,000 adults and number of rapes per 100,000 population were recorded from a data set contained in the chapter, "Sexual Stratification, Pornography, and Rape in the United States" (Baron and Straus in Pornography and Sexual Aggression) as shown below:

Playboys   8072  5785  5700  5572  5234  4920  4253  4062  3961  3846
Rapes      53.9  51.6  46.9  45.7  44.4  43.3  33.0  30.6  29.4  27.8

Playboys   3814  3745  3495  3395  3356  3339  3109  2693  2629  2501
Rapes           27.5  27.1  22.9  21.7  21.6  21.5  20.6  17.1  16.4 15.2
 
Goal of Data Analysis Lab:
Using the data set shown above, answer the following research question: 
    Is there a relationship between number of rapes and number or Playboys (predicting number of rapes given 
        the number of Playboys)?
Statistical Techniques:
  1. What type of variable is number of Playboys per 100,000 adults and number of rapes per 100,000 population?  Define the sample and population for this research question.
  2. Draw the scatterplot.  Compute the linear regression line that best fits this data set and place this equation on the scatterplot.  Compute the predicted value for 4000 Playboys.
  3. Compute and define r, the correlation coefficient.  Compute r2 and explain what this value means in the context of this research question.
  4. Compute the 95% confidence interval for the correlation coefficient.  Use this interval to answer the research question.  State what this interval estimates.
  5. Compute the five steps of hypothesis testing for the research question.
Social Commentary:
  1. Do you believe that an increase in pornography in our society is one of the factors causing an increase in the number of rapes?  How would you prove causation?
  2. Do you believe that rape is an act of male aggression over women? Explain.