Mathematical Statistics with Resampling and R

4

SAMPLING DISTRIBUTIONS

During an election year, pollsters may want to gauge how the voters feel about a particular issue. For instance, what proportion p of registered voters in a state intend to vote “Yes” on a referendum? From one random sample of size n = 1000, the pollsters might calculate a sample proportion of = 0.47. However, a different sample of the same size might have yielded = 0.49, or maybe even 0.37. To gauge the accuracy of the original estimate, we need to understand how these proportions vary from sample to sample.

In Chapter 3, we saw examples of a permutation distribution: all possible values of a test statistic obtained by permuting the data among two groups. By comparing the observed test statistic to the null distribution, we could quantify how unusual the observed test statistic was. There are many other situations where we want to know something about how a statistic varies due to random sampling.

4.1 SAMPLING DISTRIBUTIONS

Toss a fair coin n = 10 times and note the proportion of heads . If you repeat the experiment, you probably would not get exactly the ...