Right after 27 students in a college mathematics class were finished taking a test, they were asked to write down the score they thought they got on the test. After it was graded, their predicted score was subtracted from their actual score and those results are in the file PredictedScore. A positive difference means their actual score was higher than predicted and a negative difference means their actual score was lower than predicted. We will assume this sample is representative of all students that take this mathematics class. We want to see whether student predictions, on average, are less than the score they actually received. 

a. Write out the null and alternative hypotheses for our test in words or in symbols. 

b. Open the One Mean applet, choose the Bootstrapping option at the top, and paste in the data. What are the mean and standard deviation for the difference in score data? 

c. Use the applet to take at least 10,000 samples of the appropriate size from the data to develop a bootstrap sampling distribution and use the distribution to find a p-value. 

d. Based on your answer from part (c), what sort of conclusion can you make? Explain how you are determining this.