## Related questions with answers

Suppose you plan to take a random sample of 1,000 Hispanics in the United States. Assume that the distribution of origin has not changed since 2010.

a. What proportion of Hispanics in the United States in 2010 were of Mexican origin? What is the expected number of Hispanics in your sample who will be of Mexican origin?

b. What proportion of Hispanics in the United States in 2010 were of Puerto Rican origin? What is the expected number of Hispanics in your sample who will be of Puerto Rican origin?

c. Now suppose that you take a random sample of 1,000 Hispanics from your state and find 521 Hispanics of Mexican origin. A friend takes a second random sample of 1,500 Hispanics from your state and finds 847 of Mexican origin. What is the best estimate of the proportion of Hispanics in your state who are of Mexican origin?

d. Suppose you plan to take yet another random sample from your state, this time of 500 Hispanics. Based on your work in Part c, what is the best estimate of the expected number of Hispanics of Mexican origin you will find in this sample?

Solution

Verified(a) To solve for the proportion of Mexican origin from the group of Hispanics in the United States in $2010$, take a look at the given table.

In $2010$, there were a total of $50,477,594$ Hispanics in the United States. There were $31,798,258$ Mexicans among these Hispanics. Thus, the proportion is given by:

$\begin{aligned} \dfrac{\text{Mexicans}}{\text{Hispanics}}&=\dfrac{31,798,258}{50,477,594}\\ &=0.63\times100\%\\ &=63\% \end{aligned}$

Thus, $\boxed{63\%}$ of the Hispanic population are Mexicans.

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