Subject	IQ score	GPA
1	100	3.9
2	114	4
3	90	2.7
4	122	3.9
5	89	2.1
6	110	3.5
7	101	3
8	105	3.2
9	98	3
10	88	2.5
11	121	3.9
12	100	3
13	105	3.2
14	98	2.9
15	97	3
16	101	3
17	102	3.1
18	105	3.4
19	111	3.8
20	98	2.9
21	101	2.9
22	120	3.9
23	110	3.8
24	89	2.7
25	100	3.1
26	99	3.2
27	107	3.6
28	98	3.1
29	100	3.1
30	105	3.4
31	95	2.9
32	106	3.2
33	103	3.5
34	98	3.1
35	95	2.9

1. Questions.

A. Assume we know the population of this school's average GPA is 3.7 but we do not know the population's variance. Does this sample show a significantly different GPA compared to the school average? Please give the statistical test you used, degrees of freedom, the value of that test, the p-value, and your conclusion?

B. Briefly describe why the typical cut-off p-value is 0.05. Be sure to use/ explain alpha level, beta level, type 1 error, and type 2 error in your response, please?

2. Correlation/Regression Use Dataset 1

A. Run a correlation analysis of the IQ scores and GPA of this sample of students. Please report r and r² values. Is this correlation statistically significant? Please report a p value and the degrees of freedom.

B. What is the best-predicted linear regression for this correlation? Assume that the criterion is the IQ score and the predicted variable is the GPA.

C. Generate a scatter plot/ correlation matrix with IQ as the x axis and GPA as the y axis.

D. Using this regression model, what GPA would you predict a student from this school if his/her IQ score is 109?