According to researchers at Dan Jones & Associates, 1 in every 3 women has been a victim of domestic abuse (Domestic Violence: Incidence and Prevalence Study, Sept.-Dec., 2005). This probability was obtained from a survey of 1,000 adult women residing in Utah. Suppose we randomly sample 15 women and find that 4 have been abused.

a. What is the probability of observing 4 or more abused women in a sample of 15 if the proportion p of women who are victims of domestic abuse is really p = 1/3 ?

b. Many experts on domestic violence believe that the proportion of women who are domestically abused is closer to p = .10. Calculate the probability of observing 4 or more abused women in a sample of 15 if p = .10.

c. Why might your answers to parts a and b lead you to believe that p = 1/3?