A mathematics achievement test is given to students prior toentering a certain college. A sample of 10 students was selectedand their progress in calculus observed:
Student | Achievement Test Score, X | Final Calculus Grade, Y |
1 | 39 | 65 |
2 | 43 | 78 |
3 | 21 | 52 |
4 | 64 | 82 |
5 | 57 | 92 |
6 | 47 | 89 |
7 | 28 | 73 |
8 | 75 | 98 |
9 | 34 | 56 |
10 | 52 | 75 |
e) Complete the ANOVA table for the least squaresestimate for the regression line.
f) Test at the 5%significance level whether the model is useful for predicting thefinal calculus grade.
g) Give a 95%confidence interval for the mean final calculus grade when theachievement test score is 50.
h) Give a 95% prediction interval for the finalcalculus grade when the achievement test score is 50. Is theinterval wider or narrower than the confidence interval? Why?
