Question

Correlation

The following are data for 12 individuals’ daily sodium intake and their systolic blood pressure readings. A research investigator is interested in learning how strong the association is between these variables and how well we can predict blood pressure from sodium intake. Test the association at alpha 0.01.

Person


1

2

3

4

5

6

7

8

9

10

11

12



Sodium (X)

6.8

7.0

6.9

7.2

7.3

7.0

7.0

7.5

7.3

7.1

6.5

6.4

BP (Y)

154

167

162

175

190

158

166

195

189

186

148

140





1. Formulate the H0 and H1
2. C. V. at alpha 0.01 level of significance
3. Compute the test value: Pearson r, then t-value
4. Decision
5. Interpretation

Answer 1

1. Formulate the H0 and H1

H0: there is no significant association between sodium intake and blood pressure

H1: there is a significant association between sodium intake and blood pressure

2. C. V. at alpha 0.01 level of significance

The critical value at 0.01 level of significance,

$r_{(10,0.01)}=0.708$

3. Compute the test value: Pearson r, then t-value

$r=\frac{n(\sum xy)-\sum x \sum y}{\sqrt{[n\sum x^2-(\sum x)^2][n \sum y^2-(\sum y)^2]}}$

sodium(x) BP(y) x2 y2 xy

1 6.8 154 46.24 23716 1047.2

2 7 167 49 27889 1169

3 6.9 162 47.61 26244 1117.8

4 7.2 175 51.84 30625 1260

5 7.3 190 53.29 36100 1387

6 7 158 49 24964 1106

7 7 166 49 27556 1162

8 7.5 195 56.25 38025 1462.5

9 7.3 189 53.29 35721 1379.7

10 7.1 186 50.41 34596 1320.6

11 6.5 148 42.25 21904 962

12 6.4 140 40.96 19600 896

84 2030 589.14 346940 14269.8

$=\frac{(12*14269.8)-(84*2030)}{\sqrt{(12*589.14-84^2)(12*346940-2030^2)}}$ =0.9425

t=$\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$

=$\frac{0.9425\sqrt{12-2}}{\sqrt{1-0.9425^2}}$

=8.918

4. Decision

since the test statistic is greater than the critical value, the null hypothesis is rejected in favor of the alternative hypothesis.

5. Interpretation

there is a significant relationship between sodium intake and blood pressure level.