The report “New Study Shows Need for Americans to Focus on Securing Online Accounts and Backing Up Critical Data” ( PRNewswire, October 29, 2009) reported that only 25% of Americans change computer passwords quarterly, in spite of a recommendation from the National Cyber Security
Alliance that passwords be changed at least once every 90 days. For purposes of this exercise, assume that the 25% figure is correct for the population of adult Americans.
a. A random sample of size n = 200 will be selected from this population and ˆ p , the proportion who change pass-words quarterly, 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 = 200? Explain.
c. Suppose that the sample size is n = 50 rather than n = 200. 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 of 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 = 50? Explain.