(Requires computing.) If you have a large SRS, you can estimate the sampling distribution of yS by repeatedly taking samples of size n with replacement from the list of sample values. A histogram of the means from 1000 samples of size 300 with replacement from the data in Example 2.5 is displayed in Figure 2.6; the shape may be slightly skewed, but still appears approximately normal. Would a sample of size 100 from this population be sufficiently large to use the central limit theorem? Take 500 samples with replacement of size 100 from the variable acres92 in agsrs.dat, and draw a histogram of the 500 means. The approach described in this exercise is known as the bootstrap (see Efron and Tibshirani, 1993); we discuss the bootstrap further in Section 9.3.
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