Denote by p, the true proportion of people with a college degree in Ottawa/Gatin

Question

Denote by p, the true proportion of people with a college degree in Ottawa/Gatineau area. a. Let X_1 be the number of people with a college degree among a random sample of size n_1 = 20 taken from the residence of Ottawa/Gatineau. Determine the distribution of X_1 and introduce an unbiased estimator for the true parameter of interest p and name it cap p_1. b. If we choose a random sample of n_2 = 200 people horn Ottawa/Gatineau, and let X_2 be the number of those with a college degree among them then, determine the distribution of X_2 and introduce an unbiased estimator for the true parameter of interest p and name it cap p_2. c. If you arc to choose between your estimator in part (a) and part (b) to estimate p then, which one would you choose?

Explanation / Answer

(a) distribution of X1 will be binomial with parameter n1=20 and p1

SE(p1)=sqrt(p1(1-p1)/n1) and var(p1)=(p1(1-p1)/n1)

(b) distribution of X1 will be binomial with parameter n2=200 and p2

SE(p2)=sqrt(p2(1-p2)/n2) and var(p2)=(p2(1-p2)/n2)

(c) we choose (b) as its sample size is more than (a) resulting lower standard error of estimate and variance of p1

since standard error and variance is less when sample size is more

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