Wiley Series in Probability and Statistics: sampling 3rd

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Assignment 2, due Tuesday 7 February at 2:20 PM in box.
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Chapter 5, exercise 1 and 3

To estimate the proportion of voters in favor of a controversial proposition, a simple random sample of 1200 eligible voters was contacted and questioned. Of these, 552 reported that they favored the proposition. Estimate the population proportion in favor and give a 95% confidence interval for population proportion. The number of eligible voters in the population is approximately 1,800,000.
n=1200  N=1,800,000








        2.        What sample size is required to estimate the proportion of people with blood type O in a population of 1500 people to be within 0.02 of the true proportion with 95% confidence? Assume no prior knowledge about the proportion. 

N=1500    d=0.02   å=0.05





Chapter 6, exercise 1 and 3

        1.        An unequal probability sample of size 3 is selected from a population of size 10 with replacement. The y-values of the selected units are listed along with their draw-by-draw selection probabilities: y1 = 3, p1 = 0.06; y2 = 10, p2 = 0.20;y3 =7,p3 =0.10. 
(a) Estimate the population total using the Hansen-Hurwitz estimator.



          (b) Estimate the variance of the estimator.



        3.        In a water pollution study, a sample of lakes is selected from the 320 lakes in a study region by the following procedure. A rectangle of length l and width w was drawn around the study region on a map. Pairs of random numbers between 0 and 1 were generated from the uniform distribution using a random number generator on a computer. The first random number of a pair was multiplied by l and the second by w to give location coordinates within the study region. If the location was in a lake, that lake was selected. This process was continued until four of the points had fallen on lakes. The first lake in the sample was selected twice by this process, while each of the other two was selected just once. The pollutant concentrations (in parts per million) for the three lakes in the sample were 2, 5, and 10. The respective sizes of the three lakes (in km2) were 1.2, 0.2, and 0.5. In all, 80 km2 of the study region was covered by lakes. 
(a) Describe concisely the type of design used.


         (b) Give an unbiased estimate of the mean pollution concentration per lake in the population.






         (c) Estimate the variance of the estimator above.