Worksheet 21: Testing for correlation#
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Hypothesis testing conceptual inventory-taking.
a. Explain what a hypothesis test is, and why we would do it, in plain English, using 25 words or less.
b. Explain what a null hypothesis is in plain English, using 25 words or less.
c. Explain what a \(p\)-value is in plain English, using 25 words or less.
Suppose we have computed a correlation coefficient \(R\) from our data. We want to know if \(R\) 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 \(R\)?
Why could bootstrap simulation give us a good sense of variability? Will it account for outliers?