Question

(a) Assume a population’s quantitative data values are normally distributed with mean µ and standard deviation σ, and samples are simple random. Sketch 3 sampling distributions of sample means of sample size n for n = 1, n = 100, and n = 10,000, using continuous normal distribution curves. The sketches are not meant to be quantitatively precise—you just need to illustrate certain phenomena that occur as n increases. State the mean, standard deviation, and area under the curve for each of the 3 curves. Now suppose the population’s quantitative data values are uniformly distributed. As sampling size n from this population is increased, what type of distribution will the sampling distribution of sample means increasingly resemble? What famous theorem guarantees this?

Answer 1

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