1. Which will have a higher variance? please explain. a) Estimate of proportion

Question

1. Which will have a higher variance? please explain.

a) Estimate of proportion of NY state residents supporting Affortable care act. Based on a simple random sample of 2000 people.

b) Estimate of proportion of Boston residents supporting Affordable care act. Based on a simple random sample of 1000 people.

2. Considering the two surveys above, solve the following problem. Suppose the estimated support rate within Boston is pB=0.6, and the estimated support rate within NY state is pNY=0.55. Estimate the variance of the difference in teh rates of support for the Affordable care act in these two populations.

Explanation / Answer

Variance is = ( Std. deviation) ^2 / n

n is the sample size

So study mentioned in part (a) of Boston residents have higher variance

Follow the below procedure to calculate Standard deviation from given probabilities

Std. dev = sqrt([sample size][probability of success](1-[probability of success]))

So Std. dev for part (a) = sqrt ( 2000 * 0.55 * 0.45 ) = 22.25

and for study in part (b) = sqrt ( 1000 * 0.60 * 0.4 ) = 15.49

so Variance using above mentioned formula for part (a) = 22.25 ^2 / 2000 = 0.247

and for part (b) = 15.49 ^2 / 1000 = 0.24

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