based on the 2000 census, the proportion of the Californiapopulation aged 15 yea

Question

based on the 2000 census, the proportion of the Californiapopulation aged 15 years old or older who are married is p=.524 (or52.4%).
A. For random samples of N=1000 persons from this population, thestandard deviation of the sampling distribution of P*, theeproportion of married people in the sample is?
a).0158 B).0166 C).2494 D).5240
B. For the random samples of N=1000 persons from this population,the mean of the sampling distribution of P*, the proportion ofmarried people in a sample, is
a) .0158 b).0166 c).2492 d).5240
C.If the size of a sample randomly selected from a population isincreased from n=100 to n=400, then the standard deviation of P*will
a) remain the same
b)incerase by a factor of 4
c)decrease by a factor of 4
d)decrease by a factor of 2
D.Consider a random sample with sample mean (x). if the sample sizeis from N=40 to N=360, then the standard deviation of (x) will
a)remain the same
b)increase by a factor of 9 (will be multiplied by 9)
c)decrease by a factor of 9 (will be multiplied by 1/9)
d)decrease by a factor of 3 (will be multiplied by 1/3)

Explanation / Answer

Hi A) q = 1-p = 1-.524=.476 =(npq)=(1000*.524*.476)=15.79 the proportion is: 15.79/1000 = .0158 =>a B)=np = 1000*.524 = 524 proportion is 524/1000 = .524 =>d C)let n=100 and n'=400 and the new is ' => n=1/4n' we have =(npq) =(1/4n'pq)=1/2(n'pq) =1/2' => decrease by a factor of 2 =>d D)let n=40 and n'=360 and the new is ' => n=1/9n' we have =np = 1/9n'p = 1/9' => reduce by afactor of 9 => c hope this help

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