Question

1. One way of exposing under-coverage, non-response and other sources of error in sample surveys is to compare the results with known facts about the population. According to the 2010 US Census, about 1.6% of the population of the USA is Native American so the number of Native Americans in large random samples should vary approximately Normally. (a, b) What are the criteria for assessing whether a binomial sample can be approximated by a Normal distribution? (c) Based on those criteria, what minimum sample size would you expect you would require from this population, on average, in order to treat it as Normal? What are the (d) expected mean and (e) standard deviation of the proportion, p, of Native Americans in a sample, where n = 1500? Show (f, g) that use of the Normal approximation to the binomial is safe using the criteria you identified in parts (a) and (b), then, using the Normal approximation, find the probability that the sample will contain (h) 20 or fewer, (i) between 22 and 26 and (j) more than 30 Native Americans.

Answer 1

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