In a survey of college statistics students, 78 females were asked what their height was and if they could magically be any height they wanted, what their magical height would be. Both of these numbers were given in inches. We want to determine whether there is strong evidence of a positive association between actual height and magical height. The data can be found in MagicalHeight. 

a. State the null and alternative hypotheses. 

b. Use the Corr/Regression applet to find and report the least squares regression line. 

c. Is the association between actual height and magical height positive? How do you know? 

d. What could you say about magical heights compared to actual heights if the slope of the least square regression line were negative? 

e. What is the p-value for the simulation-based test for slope?

f. Is there strong evidence of a positive association between height and magical height? 

g. What can you conclude about generalization and causation from your results?