3. Nine different students were given version A of a test designed to measure their critical thinking skills. The students then took a course in critical thinking. At the end of the course the students took version B of the same test. You are asked to determine if the course was effective in improving their scores.
Student 1 2 3 4 5 6 7 8 9
(Before) A 48 52 58 44 43 43 40 51 59
(After) B 73 67 73 59 58 56 58 64 74
a) (2) Construct a scatter-plot for the test data (in the grid above).
b) (2) Find the correlation coefficient ________ and the coefficient of determination ____________.
c) (1) Interpret the coefficient of determination. ______________________________________________
d) (1) Is the correlation coefficient significant at the .05 level of significance? _________________
e) (2) How would you describe the correlation between the two test scores?
f) (3) Use the sample test data to find the equation of the regression line that would be used to predict a score (on B) after taking the course using the score (A) on the test given before the course. Round both coefficients to 3 decimal places.
g) (2) Draw the regression line on the grid above (use the results from part e).
h) (2) Use the regression equation to predict the score after the course (B) for a student who had a score of 40 on A before the course. Show equation work for credit.
i) (2) What is the residual for Student number 8? Did this student do better or worse than predicted on test B?
j) (2) Why can't you predict a Version B score for a student who had a Version A score of 89 ?
The solution provides step by step method for the calculation of regression analysis and test statistic for significance of correlation coefficient. Formula for the calculation and Interpretations of the results are also included.