Chapter 8, Problem 8.112ACI

State SAT scores. Refer to Exercise 2.27 (p. 60) and the data on average math SAT scores for each of the 50 states and District of Columbia for the years 2014 and 2010. 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.)

State	2014	2010
Alabama	533	550
Alaska	503	513
Arizona	525	524
Arkansas	571	564
California	510	516
Wisconsin	608	603
Wyoming	599	565

1. a. In Exercise 2.27c, you computed the paired differences of SAT scores by subtracting the 2010 score from the 2014 score for each state. Find the mean of these 51 paired differences. This value is μ_d, the mean difference in SAT scores for the population of 50 states and the District of Columbia. .20
2. b. Explain why there is no need to employ the confidence interval or test procedures of this section to make an inference about μ_d.
3. 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 2014 differs from the true mean in 2010. Use a confidence level of .90.