# Hw8 - N = 3078 counties and county-equivalents in the United States We have data agsrs.dat from an SRS of 300 of the 3078 counties containing the

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Stat 201A HW8: Due Wednesday, November 24, 2010 (in class) 1. This exercise considers a small population to compare the three estimators for unequal prob- ability sampling. Suppose we have a population of N = 2 units with y 1 = 9 and y 2 = 1. (a) We take random samples with replacement of size n = 2 with selection probability p 1 = . 8 and p 2 = . 2. So there are total 2 × 2 = 4 possible samples. For each sample s = ( i, j ), i, j = 1 , 2, compute P ( s ), ˆ τ p , ˆ τ π and ˆ τ g . Then compute the mean, variance and mean square error (MSE) for each estimator. [Hint: read section 6.4 small population example.] (b) Repeat part (a) with p 1 = . 6 and p 2 = . 4. (c) Repeat part (a) with p 1 = . 3 and p 2 = . 7. (d) What do you learn from this exercise? 2. The U.S. government conducts a Census of Agriculture every ﬁve years, collecting data on all farms in the 50 states. The Census of Agriculture provides data on number of farms, the total acreage devoted to farms, farm size, yield of di±erent crops, and a wide variety of other agricultural measures for each of the
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Unformatted text preview: N = 3078 counties and county-equivalents in the United States. We have data ( agsrs.dat ) from an SRS of 300 of the 3078 counties containing the 1982, 1987 and 1992 information on the number of farms, acreage devoted to farms and etc. Suppose we know the population totals for 1987 but only have 1992 information on the SRS of 300 counties. In 1987 the U.S. had a total of 2 , 087 , 759 farms. (a) Plot ACRES92 against FARMS87. Comment on the plot. (b) Use ratio estimation to estimate the total number of acres devoted to farming in 1992 (ACRES92), using the number of farms in 1987 (FARMS87) as the auxiliary variable. Give the standard error. (c) Repeat part (b), based on a model. Perform diagnostics and comment on the model assumptions. (d) Repeat part (b), using regression estimation. (e) Repeat part (d), based on a model. Perform diagnostics and comment on the model assumptions. 1...
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## This note was uploaded on 11/24/2010 for the course STAT 201a taught by Professor Wu during the Spring '10 term at Pasadena City College.

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