People 65 years and older are the fastest growing segment of the US population,

Question

People 65 years and older are the fastest growing segment of the US population, and constituted 13% of the population in 2010.1 The figure below shows sample proportions from two sampling distributions of the proportion 65 years and older in the US: One shows samples of size 100, and the other shows samples of size 1000 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 021 023 0.25 Proportion Age 65+ (n=100) 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 023 0.25 Proportion Age 65+ 1000) (a) What is the center of both distributions? Round your answers to two decimal places. Center for n 100 Center for n = 1000: (b) What is the approximate minimum and maximum of each distribution? Round your answers to two decimal places. For the 100 distribution: minimum maximum

Explanation / Answer

(a) Center for both distribution

for n = 100 => Center = 0.13

for n = 1000 = > Center = 0.13

(b) Minimum for n = 100 => Minimum = 0.05

Maximum for n = 100 => Maximum = 0.25

Minimum for n = 1000 => Minimum = 0.10

Maximum for n = 1000 => Maximum = 0.16

(c) Standard error for n = 100

SE = Sqrt [p * (1-p)/n] = sqrt [ 0.13 * 0.87/100] = 0.0336

Standard error for n = 1000

SE = Sqrt [p * (1-p)/n] = sqrt [ 0.13 * 0.87/1000] = 0.0106

(D) No, It would not be surprizing to see from a sample size 100 as the proportion of 0.17 is under the value of minimum and maximum value.

Yes, it would be sureprizing to see from a sample size 1000 as the proportion of 0.17 is under the value of minimum and maximum value.

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