Suppose an article reported that 14% of unmarried couples in the United States a

Question

Suppose an article reported that 14% of unmarried couples in the United States are mixed racially or ethnically. Consider the population consisting of all unmarried couples in the United States. (a) A random sample of n = 150 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? (Round your answer for up to two decimal places and your answer for op to four decimal places.) (b) Is it reasonable to assume that the sampling distribution of p is approximately normal for random samples of size n = 150? Explain. because np 10 and n(1 - p) 10. (c) Suppose that the sample size is n = 300 rather than n = 150, as in Part (b). What are the values for the mean and standard deviation? (Round your answer for mu_p to two decimal places and your answer for sigma_p to four decimal places.) (d) Is it reasonable to assume that the sampling distribution of p is approximately normal for random samples of size n = 300? Explain. because np ? 10 and n(1 - p) ?10. (e) When n = 150, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17? (Round the answer to four decimal places. Type NONE if it is not appropriate to use the normal distribution.) When n = 300, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17? (Round the answer to four decimal places. Type NONE if it is not appropriate to use the normal distribution.)

Explanation / Answer

a) mean = p = 0.14 = 0.14
standard devation = sqrt(p*(1-p)/n) = sqrt(0.14*0.86/150) = 0.02833137 = 0.0283

b) yes, beacuse np > 10 and n(1-p) > 10

c) mean = p = 0.14 = 0.14
standard devation = sqrt(p*(1-p)/n) = sqrt(0.14*0.86/300) = 0.0200333

d) yes, beacuse np > 10 and n(1-p) > 10

e) z = (x-mean)/(std dev) = (0.17 - 0.14)/0.0283314 = 1.0589
p(z>1.0589) = 1 - 0.8552 = 0.1448

f) z = (x-mean)/(std dev) = (0.17 - 0.14)/0.0200333 = 1.497506651
p(z>1.4975) = 1 - 0.9329 = 0.0671

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