From the values 1 to 50, 10 numbers are selected without replacement and we start from those 10 numbers to get 10 samples of 1-in-50 systematic samples. We will select 10 repeated samples with 8 samples in each, so we choose 1-in-400/8 = 50. How do we obtain the random numbers for repeated systematic sampling? Use the data given in the following table to estimate the average number of persons per car and also provide an estimate of the variance. To facilitate the estimation of the variance of the systematic sample the investigator chooses to use repeated systematic sampling with 10 samples of 8 cars each. The company knows from last year that 400 cars took the ferry and they want to sample 80 cars. The ferry company wants to estimate the average number of people per car for August. ( see p.247 of Scheaffer, Mendenhall and Ott)Ī ferry that carries cars across a bay charges a fee by carload rather than by a person. Thus, we need more than one primary unit. Unless the population is randomly ordered we can't use the naive method to compute the variance. When the population is periodic, the systematic sampling may be worse than the simple random sampling and the above formula will underestimate the variance since if the period k is chosen poorly, then the elements sampled may be too similar to each other. However, when the population is ordered, systematic sampling is usually better than simple random sampling and the above formula will overestimate the variance. How do we estimate the variance of this single systematic sample? We can pick a starting point randomly from 1 to 600 and sample every 7th student from that on until we have reached 1200 samples. Since, 9000/1200 = 7.5, we can perform a 1-in-7 systematic sample. How do we sample these students systematically? Example: Suppose our population is 9,000 students and we want to sample 1,200 students.
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