Question
In: Statistics and Probability
A university is concerned about the presence of grade inflation, which is defined as an increase...
|
A university is concerned about the presence of grade
inflation, which is defined as an increase in the 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 the past 11 Year GPA 1 3.07 2 . 2.88 3 2.97 4 2.87 5 2.99 6 3.05 7 3.07 8 3.01 9 3.19 10 3.15 11 3.14 Construct a 95% confidence interval for the slope. LCL= and UCL= |
Solutions
Expert Solution
Solution:
We have to find a 95% confidence interval for the regression
slope.
Formula:
where
Thus we need to make following table:
| x: year | y: GPA | x^2 | y^2 | xy |
| 1 | 3.07 | 1 | 9.4249 | 3.07 |
| 2 | 2.88 | 4 | 8.2944 | 5.76 |
| 3 | 2.97 | 9 | 8.8209 | 8.91 |
| 4 | 2.87 | 16 | 8.2369 | 11.48 |
| 5 | 2.99 | 25 | 8.9401 | 14.95 |
| 6 | 3.05 | 36 | 9.3025 | 18.3 |
| 7 | 3.07 | 49 | 9.4249 | 21.49 |
| 8 | 3.01 | 64 | 9.0601 | 24.08 |
| 9 | 3.19 | 81 | 10.1761 | 28.71 |
| 10 | 3.15 | 100 | 9.9225 | 31.5 |
| 11 | 3.14 | 121 | 9.8596 | 34.54 |
 |
 |
 |
 |
 |
Thus
Thus
Thus
Thus
where tc is t critical value for c =95% confidence level.
df = n - 2 = 11 - 2 = 9
Look in t table for df = 9 and two tail area = 1 - 0.95 = 0.05
Thus from t table: tc = 2.262
Thus
Thus
Thus
LCL = 0.0055
UCL = 0.0391
orchestra answered 1 year agoRelated Solutions
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