how do you calculate all parts of this question? An article reported that 9% of
ID: 3132481 • Letter: H
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how do you calculate all parts of this question?
An article reported that 9% 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 random sample of n = 50 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.) is it reasonable to assume that the sampling distribution of p is approximately normal for random samples of size n = 50? Explain. Suppose that the sample size is n = 200 rather than n = 50, 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 = 200? (Round your standard deviation to four decimal places.)Explanation / Answer
(a)The mean of the sampling distribution p^ is 0.09.
The standard deviation p(1-p)/n=0.09(1-0.09)/50=0.04
(b)Calculate np=0.09*50=4.5
Np(1-p)=4.095
Thus the distribution is not approximately normal as np<10
(c)The mean 0.09.
The standard deviation p(1-p)/n=0.09(1-0.09)/200=0.02
(d)Calculate np=0.09*200=18
Thus the distribution is approximately normal as np>10
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