Hello,

Could you review my work and let me know if I did this correctly? Thanks, I really appreciate it!

The table is not displaying correctly.

Here are the totals:

(X-Xbar)squared = 148.136

(Y-Ybar)squared = 5208.1

(X-Xbar)(Y-Ybar) = -475.2600

Part One: Pearson Correlation

Suppose that we are interested in the strength of association between the number of skin cancer mortality per year (the dependent variable Y) and latitude (the independent variable X) among 10 states in the US. The number of skin cancer mortality per year and the latitude of each location were provided in the table below:

States

Latitude (X)

Mortality (Y)

X-Xbar

(X-Xbar)²

Y-Ybar

(Y-Ybar)²

(X-Xbar)(Y-Ybar)

Alabama

33

219

-2.98

8.8804

36.3

1317.69

-108.1740

Arizona

34.5

160

-1.48

2.1904

-22.7

515.29

33.5960

Arkansas

35

170

-0.98

0.9604

-12.7

161.29

12.4460

California

37.5

182

1.52

2.3104

-0.7

0.49

-1.0640

Colorado

39

149

3.02

9.1204

-33.7

1135.69

-101.7740

Connecticut

41.8

159

5.82

33.8724

-23.7

561.69

-137.9340

Delaware

39

200

3.02

9.1204

17.3

299.29

52.2460

Wash,D.C.

39

177

3.02

9.1204

-5.7

32.49

-17.2140

Florida

28

197

-7.98

63.6804

14.3

204.49

-114.1140

Georgia

33

214

-2.98

8.8804

31.3

979.69

-93.2740

Total

148.136

5208.1

-475.2600

From Dawson and Trapp, we know that the formula for the Pearson product moment correlation coefficient is:

1)Using the information in the table provided, calculate correlation coefficient (r) and show your work.

r = -0.5422

2)Interpret the size of r in two ways. First, give your interpretation the index value both in terms of direction (positive or negative) and strength (weak, moderate, or strong). Second, give your interpretation if the squared value of r.

The index value, r = -0.5422 of correlation show a moderate negative relationship between the variables.

r squared = 0.2940

This shows 29.40% of the mean variability.

Additional 7 states (Idaho, Illinois, Indiana, Iowa, Kansas, Kentucky, and Louisiana) were enrolled in the study (total states = 17). The latitude and number of skin cancer mortality per year were collected. We analyze the data using SAS's CORR procedure and observe the result shown in table 1 (see page 6). Based on those findings, answer the following questions.

3)Identify the dependent variable and the independent or explanatory variable in this study. Also, state the Null and Alternative hypotheses.

Dependent value: State

Independent value: Latitude

H₀: There is no association (Independent)

H_A: There is association (dependent)

4)Report the correlation coefficient and P-value that should be used to test the Null hypothesis. Based on that information, what conclusion can you make about the Null hypothesis? (i.e. Reject or Fail to Reject the Null).

Correlation coefficient = -0.74307 which shows moderate negative association between the variable.

p value = 0.0006

I will reject the null hypothesis since p-value, 0.0006 < .05, and conclude that there is a relationship that exists between the variables.