State Math SAT Scores. Refer to the SPSS simple linear regression relating y = average state SAT Math score in 2014 with x = average state SAT Math score in 2010, Exercise 11.19 (p. 654).

a. Give the null and alternative hypotheses for determining whether a positive linear relationship exists between y and.

b. Locate the -value of the test on the SPSS printout. Interpret the result if Â = .05.

c. Find a 95% confidence interval for the slope, _{1}. Interpret the result

Exercise 11.19

State Math SAT scores. Refer to the data on average state Math SAT scores for 2010 and 2014, Exercise 2.27 (p. 84). The first five observations and last two observations in the file are reproduced in the next table. In Exercise 2.128 (p. 132), you examined the relationship between the 2010 Math SAT scores and the 2014 Math SAT scores with a scatterplot.

a. Write the equation of a straight-line model relating 2014 Math SAT score (y) to 2010 Math SAT score (x). An SPSS simple linear regression printout for the data is shown. Find the least squares prediction equation.

b. Give a practical interpretation of the y-intercept of the least squares line. If a practical interpretation is not possible, explain why.

c. Give a practical interpretation of the slope of the least squares line. Over what range of x is the interpretation meaningful?

Exercise 2.128

State SAT scores. Refer to Exercise 2.27 (p. 84) and the data on state SAT scores. Construct a scatterplot for the data, with 2010 Math SAT score on the horizontal axis and 2014 Math SAT score on the vertical axis. What type of trend do you detect?

Exercise 2.27

State SAT scores. Educators are constantly evaluating the efficacy of public schools in the education and training of American students. One quantitative assessment of change over time is the difference in scores on the SAT, which has been used for decades by colleges and universities as one criterion for admission. Originally, the SAT provided scores in reading and mathematics. Now, three scores are provided: reading, mathematics, and critical writing. SAT scores for each of the 50 states and District of Columbia for the years 2014 and 2010 are saved in the accompanying file. Data for the first five and last two states are shown in the table on the next page.

a. Use graphs to display the SAT mathematics score distributions in 2014 and 2010. How did the distributions of state scores change over the 5-year period?

b. As another method of comparing the 2014 and 2010 SAT mathematics scores, compute the paired difference by subtracting the 2010 score from the 2014 score for each state. Summarize these differences with a graph. Compare the results with those of part a.

c. Based on the graph, part b, what is the largest improvement in SAT mathematics score? Identify the state associated with this improvement.