Question

An article reported that 5% 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 = 150 couples will be selected from this population and p̂, 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 p̂? (Round your standard deviation to four decimal places.)

mean

standard deviation

(b) Suppose that the sample size is n = 250 rather than n = 150, as in Part (b). Does the change in sample size change the mean and standard deviation of the sampling distribution of p̂? What are the values for the mean and standard deviation when n = 250? (Round your standard deviation to four decimal places.)

mean

standard deviation

(c) When n = 250, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.08? (Round your answer to four decimal places.)

Answer 1

a) For n = 150,

The mean of the sampling distribution of p̂ =

The standard deviation of the sampling distribution of p̂ =

b) For n = 250,

The mean of the sampling distribution of p̂ =

The standard deviation of the sampling distribution of p̂ =

Change in sample size does not  change the mean of the sampling distribution of p̂ but it will decrease the standard deviation.

c) Here,

The probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.08