Question

A university is concerned about the presence of grade inflation, which is defined as an increase in the Year average GPA of the institution's students over time without a comparable increase in academic standards. To investigate this phenomenon, the average GPA for the student body was recorded over 2 the past 11 years, as shown in the table to the right. Construct a 90% confidence interval for the regression slope GPA 3.08 2.87 2.98 2.86 2.97 3.03 GPA 3.07 2.99 3.21 Year 10 3.17 Construct a 90% confidence interval for the slope LCL-D and UCL (Round to three decimal places as needed.)

Answer 1

(x-x) (y-y) -0.2318 0.6545 0.1609 0.3473 0.0636 0.0000 0.0364 0.0873 0.5291 0.4255 0.6818 2.5800 (x-x) (y-y) 0.0021 0.0268 0.0029 0.0301 0.0040 0.0000 0.0013 0.0019 0.0311 0.0113 0.0186 0.1303 S.No 1 2 25.0000 16.0000 9.0000 4.0000 1.0000 0.0000 1.0000 4.0000 9.0000 16.0000 25.0000 110.0000 SSX 1 3.08 2.87 2.98 2.86 2.97 3.03 3.07 2.99 3.21 3.14 3.17 33.37 3.0336 2 4 10 10 Total Mean 6.0000 SSY sample size: here 3.0336 6.0000 from above 110.0000 2.5800 slope- 0.0235 intercept- 2.8929 0.0697 error variance σ2- s' -SSE/(n-2) 0.008 std error σ 0.0880 estimated standard error of slope se(B1) 0.0084 for 90 % Cl value of t margin of error E-t std error lower confidence bound-estimated slope-margin of error- Upper confidence bound-estimated slope+margin of error- 1.8330 0.015 0.008 0.039

from above

LCL =0.008

UCL =0.039