Chapter 7, Section 7.3, Question E38 According to the U.S. Census Bureau, 22.3 p

Question

Chapter 7, Section 7.3, Question E38 According to the U.S. Census Bureau, 22.3 percent of the Spanish-surnamed population in the United States have one of these surnames: Garcia, Martinez, Rodriguez Lopez, Hernandez, Gonzalez, Perez, Sanchez, Rivera, Ramirez, Torres, Gonzales. Suppose you take a random sample of 500 Spanish-surnamed people in the United States [Source: David L. Word and R. Colby Perkins Jr., Building a Spanish Surname List for the1990's-A New Approach to an Old Problem, Technical Working Paper no. 13, March 1996.] a. Suppose you take a random sample of 120 Spanish-surname people. Describe the shape, find the center and spread of the sampling distribution of the proportion of people in your sample with one of the given surnames. The shape is The center The spread (round to four decimal places) b. With a sample of size 120, will the probability of getting 20% or fewer with one of the given surnames be larger or smaller than the probability you computed with sample size 500? The probability of getting 20% or fewer in the sample will be with a sample size of 120

Explanation / Answer

a) Shape is Bell or symmetric

Center = p = 0.223

Spread = sqrt(pq/n) = sqrt( 0.223 * (1-0.223) / 120) = 0.038

b) P( p < 0.20) = P(Z < (0.20 - 0.223) / 0.038) =P(Z < -0.6053) = 0.2725

The proability that getting 20% of fewer in the sample will be 0.2725 wtha a smaple size of 120

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