# Worksheet 21: Testing for correlation

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1. **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.
    

2.  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 $R$?

    


3. Why could bootstrap simulation give us a good sense of variability? Will it account for outliers?