An article reported that 8% of married couples in the United States are mixed ra

Question

An article reported that 8% 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 = 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? (Round your standard deviation 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 = 100? Explain.

Yes, because np < 10 and n(1 p) < 10. Yes, because np > 10 and n(1 p) > 10.    No, because np < 10.No, because np > 10.

(c) Suppose that the sample size is n = 250 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? What are the values for the mean and standard deviation when n = 250? (Round your standard deviation 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 = 250? Explain.

Yes, because np < 10. Yes, because np > 10. No, because np < 10.No, because np > 10.

(e) 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 0.09? (Round your answer to four decimal places.)

Explanation / Answer

a)as per central limit theorum

mean phat=population mean p =0.08

std deviation =(p(1-p)/n)1/2 where n=100

=0.0271

b) No, because np < 10

c)mean phat=0.08

and standard deviation will change as n is changing in above formula

hence

std deviation =(p(1-p)/n)1/2 where n=250

=0.0172

d) Yes, because np > 10

e)here as z=(phat-p)/std deviation

hence P(X>0.09) =1-P(X<0.09) =1-P(Z<(0.09-0.08)/0.0172) =1-P(Z<0.5828) =1-0.7200 =0.2800

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.