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
​years, as shown in the table to the right. Construct a 95​% confidence interval for the regression slope.

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


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