Chapter 7, Section 7.3, Question P14 In the 2000 U.S. Census, 53% of the populat

Question

Chapter 7, Section 7.3, Question P14 In the 2000 U.S. Census, 53% of the population over age 30 were women. [Source: U.S. Census Bureau, www.census.gov.] a. Describe the shape, mean, and standard error of the sampling distribution of P, the proportion of women in the sample, for random samples of size 120 taken from this population. The sampling distribution is approximately Mean Standard error - (round to two decimal places) Make an accurate sketch, with a scale on the horizontal axis of this distribution. 0.40 045 0.50 0.35 0.60 0.65 Fig. 1 0.40 0.45 0.50 0.55 0.60 0.65 Fig. 3 0.40 0.45 0.50 0.55 0.60 0.65 Fig. 4 0.40 0.45 0.50 0.55 0.60 0.65 Fig. 2 Input the number of the correct figure. b. To be a member of the U.S. Senate, you must be at least 30 years old. In 2000, 9 of the 100 members of the u.S. Senate were women. Is this a reasonably likely event if gender plays no role in whether a person becomes a U.S. Senator?

Explanation / Answer

Answer to the question is as follows, with explanation and formule. Dont hesitate to give a "thumbs up" in case you're satisfied with the answer:

a. The distribution is fairly normal as

np =120*.53>10

n(1-p) = 120*.47>10

Mean = np = 120*.53 = 63.60

Standard error = sqrt(p*p'/n) = sqrt(.53*.47/120) = 0.05

Accurate sketch : Figure 1: because : it's deviation is .05 ( figure 4 is normal but has a much lesser deviation)

Answer is 1

b. p^= .90

Z = (p^-p)/sqrt(p*p'/n) = (.9-.53)/sqrt(.53*.47/120) = 8.121

Since this Z statistic is pretty more than 3, we conclude that gender does play a role in whether a person becomes a U.S Senetor.

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