The article “Unmarried Couples More Likely to Be Interracial” (San Luis Obispo Tribune, March 13, 2002) reported that 7% of married couples in the United States are mixed racially or ethnically. Consider the population consisting of all married couples in the United States.
a. A random sample of n = 100 couples will be selected from this population and ˆ p, the proportion of couples that are mixed racially or ethnically, will be computed. What are the mean and standard deviation of the sampling distribution of ˆ p?
b. Is the sampling distribution of ˆ p approximately normal for random samples of size n = 100? Explain.
c. Suppose that the sample size is n = 200 rather than n = 100. Does the change in sample size affect the mean and standard deviation of the sampling distribution of ˆ p ? If so, what are the new values for the mean and standard deviation? If not, explain why not.
d. Is the sampling distribution of ˆ p approximately normal for random samples of size n = 200? Explain.