Worksheet 21: Testing for correlation#
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Suppose we have computed a correlation coefficient \(\hat R\) from our data. We want to know if \(\hat R\) reflects an actual trend, or if it is just noise.
Null hypothesis: the pairs \((x_i,y_i)\) are paired up totally randomly.
a. Why is this null hypothesis saying that there is no real correlation?
b. In plain English, what is the \(p\)-value of \(\hat{R}\)?
Why could bootstrap simulation give us a good sense of variability? Will it account for outliers?
Will bootstrap simulation always give us a good idea of the variability of \(\hat R_n\)?
Are we sure the bootstrap confidence interval is accurate for the population distribution of all Stanford students?