Consider the following data of 20 students on their highscho

Consider the following data of 20 students on their high-school GPA and undergraduate GPA when they graduated.

Student number

High-school GPA

Undergraduate GPA

1

2.83

3.59

2

3.31

3.11

3

3.50

2.75

4

3.29

3.33

5

3.13

2.84

6

2.81

3.30

7

3.19

3.05

8

3.49

3.28

9

2.93

2.87

10

3.14

3.50

11

3.00

2.72

12

2.95

2.73

13

2.93

3.08

14

2.89

2.81

15

2.76

2.89

16

2.82

3.02

17

3.00

3.27

18

3.13

3.10

19

3.37

2.93

20

3.30

3.07

Use Excel to calculate the correlation between high-school GPA and undergraduate GPA.

Conduct a hypothesis test with the following hypothesis (use alpha value of 0.05):        

Null hypothesis: The correlation between high-school GPA and undergraduate GPA is zero.

Alternate hypothesis: The correlation between high-school GPA and undergraduate GPA is not zero.

Answer the following questions:

What is the p-value and how do you interpret it?

What does the alpha value signify?

What is a type-1 error in this case?

What do you conclude as a result of the test?

Student number	High-school GPA	Undergraduate GPA
1	2.83	3.59
2	3.31	3.11
3	3.50	2.75
4	3.29	3.33
5	3.13	2.84
6	2.81	3.30
7	3.19	3.05
8	3.49	3.28
9	2.93	2.87
10	3.14	3.50
11	3.00	2.72
12	2.95	2.73
13	2.93	3.08
14	2.89	2.81
15	2.76	2.89
16	2.82	3.02
17	3.00	3.27
18	3.13	3.10
19	3.37	2.93
20	3.30	3.07

Solution

Correlation Matrix High-school GPA Undergraduate GPA High-school GPA 1.000 Undergraduate GPA .002 1.000 20 sample size