北美数学代写_数学入学考试代写 Mid-term test/ MAT3377

Mid-term test/ MAT3377
Surveys and Sampling
Fall 2013.

数学入学考试代写 Estimate the total proportion of illegally parked car in this city. If tickets of $40.00 are issued for all the illegally parked ……

Calculators are permitted. This is an open book exam.  数学入学考试代写

1. In a small city with the population size of N=8500 families a simple random sample of n = 15 families are taken and the number of family members in each of the 15 families are
   3, 4, 4, 2, 1, 8, 2, 1, 1, 2, 3, 3, 5, 2, 6

[17] (i) Estimate the proportion of single families in this city and place a bound on your estimate.

[17] (ii) Use the above sample of size 15 as a presample to find an appropriate sample size for a simple random sample to estimate the average family size in this city with a margin of error of 0.8.

1. The following observations are marks of N = 5 students in a class. 19, 17, 14, 15, 17

(i) [7] How many distinct sample of size n = 2 do we have ? List all these possible distinct samples of size 2.
(ii)[15] Prove E(s 2 ) = S 2 by using all the possible distinct samples in the previous part (part (i)).

4. [10] Why should we prefer simple random sampling without replacement compare to sampling with replacement ? Explain in details and justify your conclusions rigorously.  数学入学考试代写

1. A city is divided into L = 2 areas and there are N = 1000 blocks in these areas. A stratified sample was selected from city blocks. In areas 1, 2 and there are N1 = 400 and N2 = 600 blocks respectively. Let x be number of cars parked on the street and y be the number of illegally parked cars on the street. Samples of n1 = 9 and n2 = 10 are taken from each of L = 2 areas respectively and the results are summarized in the following two tables.

Area 1

Area 2

17 Estimate the total number of cars parked on the street in the city and place a bound on your estimate.

[17] (ii) Estimate the total proportion of illegally parked car in this city. If tickets of $40.00 are issued for all the illegally parked cars in this city, estimate the totla city’s income from these tickets and place a bound on your estimate.

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