The data on average math SAT scores for each of the 50 states and District of Columbia for the years 2001 and 2011. The data are saved in the file. (The first five observations and last two observations in the data set are shown in the table below.)
For Information: Refer to Exercise 2.27

a. In Exercise 2.27c, you computed the paired differences of SAT scores by subtracting the 2001 score from the 2011 score for each state. Find the mean of these 51 paired differences. This value is µd the mean difference in SAT scores for the population of 50 states and the District of Columbia.
b. Explain why there is no need to employ the confidence interval or test procedures of this section to make an inference about µd.
c Now, suppose the 50 paired differences of part a represent a sample of SAT score differences for 50 randomly selected high school students. Use the data in the file to make an inference about whether the true mean SAT score of high school students in 2011 differs from the true mean in 2001. Use a confidence level of .90.

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State 2001 2011 Alabama Alaska Arizona Arkansas California 554 510 525 550 541 511 523 570 Wisconsin Wyoming 596 545 602 569