Sunday, December 4, 2011

Statistics question about simple random samples?

Problem 3. A simple random sample of size nine is drawn from a population of 4000 high school students. The students in the sample are administered IQ tests; the other students are not. The IQs of the students in the sample are





IQ


79.58


100.46


100.27


103.95


124.82


108.17


100.54


105.4


101.95





The sample mean of the IQ scores is ______





The collection of IQ scores of all 4000 students is a (real OR fictitious) population.





The sample mean is a(n) (biased OR unbiased) estimator of the mean IQ score of the population of students.





The sample standard deviation of the IQ scores is _________





The sample standard deviation is a(n) (biased OR unbiased) estimator of the standard deviation of the population.





The finite population correction is ________





The estimated standard error of the sample mean of the IQ scores is _________|||The sample mean of the IQ scores is 102.7933





The collection of IQ scores of all 4000 students is a real population.


The sample mean is a(n) unbiased estimator of the mean IQ score of the population of students.


The sample standard deviation of the IQ scores is 134.8343





The sample standard deviation is a(n) unbiased estimator of the standard deviation of the population.


(so long as you divide the sum of squared deviations from the mean by 8 and not by 9)





The finite population correction is


sqrt [ (N-n)/(N-1) ] = sqrt[ (8000-9)/(8000-1)] = .9996





The estimated standard error of the sample mean of the IQ scores is = sd/sqrt(9)


= 134.8343/3 = 44.9448

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