The company Digital Trends reported that 48% of Americans have shared passwords for TV and movie streaming. + For purposes of this exercise, assume that the 48% figure is correct for the population of adult Americans. (a) A random sample of size n = 400 will be selected from this population and p, the proportion who have shared TV and movie streaming passwords, will be calculated. What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.) mean standard deviation (b) Is the sampling distribution of p approximately normal for random samples of size n = 400? Explain. The sampling distribution of p is approximately normal because np is less than 10. The sampling distribution of p is approximately normal because np and n(1 - p) are both at least 10. The sampling distribution of p is not approximately normal because np is less than 10. The sampling distribution of p is not approximately normal because np and n(1 - p) are both at least 10. The sampling distribution of p is not approximately normal because n(1 - p) is less than 10. (c) Suppose that the sample size is n = 100 rather than n = 400. What are the values of the mean and standard deviation when n = 100? (Round your standard deviation to four decimal places.) mean standard deviation Does the change in sample size affect the mean and standard deviation of the sampling distribution of p? If not, explain why not. (Select all that apply.) When the sample size decreases, the mean increases. When the sample size decreases, the mean decreases. When the sample size decreases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size decreases, the standard deviation increases. When the sample size decreases, the standard deviation decreases. When the sample size decreases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size. (d) Is the sampling distribution of p approximately normal for random samples of size n = 100? Explain. The sampling distribution of p is approximately normal because np is less than 10. The sampling distribution of p is approximately normal because np and n(1 - p) are both at least 10. The sampling distribution of p is not approximately normal because np is less than 10. The sampling distribution of p is not approximately normal because np and n(1 - p) are both at least 10. The sampling distribution of p is not approximately normal because n(1 - p) is less than 10
