Chapter 7, Section 7.3, Question P14 In the 2000 U.S. Census, 53% of the populat
ID: 2947055 • Letter: C
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
a)
Sampling distribution is normal
mean = 0.53
standard error = sqrt( p*(1-p)/n)
= sqrt(0.53 *(1-0.53)/120)
= 0.0456
Figure 1)
b)
P(X < 0.09)
= P(z < (0.09 - 0.53)/0.0456)
= P(z < -9.65)
= 0.0000
As the probability is significantly less, we can say that the event is not likely if gender plays no role.