The article referenced in Exercise 8.25 reported that for unmarried couples living together, the proportion that are racially or ethnically mixed is .15. Answer the questions posed in Parts (a)– (e) of Exercise 8.25 for the population of unmarried couples living together.
In Exercise 8.25
a. A random sample of n = 100 couples will be selected from this population and 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 p^ ?
b. Is it reasonable to assume that the sampling distribution of p^ is approximately normal for random samples of size n = 100? Explain. np , 10.
c. Suppose that the sample size is n = 200 rather than n = 100, as in Part (b). Does the change in sample size change the mean and standard deviation of the sampling distribution of p^? If so, what are the new values for the mean and standard deviation? If not, explain why not.
d. Is it reasonable to assume that the sampling distribution of p^ is approximately normal for random samples of size n = 200? Explain.
e. When n = 200, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10?