Does having a professor show up late for class influence students to be late for class? Or when professors are early, do students tend to show up early? In the spring of 2008, some statistics students randomly chose 31 different classes and recorded how many minutes a professor was early or late for class and the average number of minutes the students in the class were early or late. They wanted to see if there was a positive linear relationship between the professor€™s and the students€™ arrival times. We input these data into statistical soft ware and found the correlation was 0.227. We then shuffled the data 1,000 times and found the corresponding 1,000 correlations. The simulated correlations are shown in the graph for Exercise 10.CE.13.

a. What is the null hypothesis in this study?
b. What is the alternative hypothesis in this study?
c. Which variable would it seem is the explanatory variable and which is the response?
d. Based on the histogram, what is the approximate p-value for this study?
e. What would be your complete conclusion for the one sided study?
f. If this were a two-sided test, how would the alternative hypothesis change and what would be the new approximate p-value?
g. Even if you conclude that the association between these variables is statistically significant, can you legitimately conclude that the instructor€™s being late caused students to be late? Explain.

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