Can a pretest on mathematics skills predict success in a statistics course? the 55 students in an introductory statistics class took a pretest at the beginning of the semester. the least-squares regression line for predicting the score y on the final exam from the pretest score x was y = 10.5 + 0.82x . the product of 0.82 times x (the pre-test score) + 10.5 predicts the score on the final exam, y. the standard error of b was 0.38. test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative.

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above