Question

A food company has developed a high mineral sea salt (sodium). A nurse practitioner hypothesizes that getting more sodium from the new sea salt predicts an increase in blood pressure. Below are the sodium and BP measurements for a sample of participants that regularly use the new sea salt. What can the nurse practitioner conclude with an α of 0.10?

Sodium	BP
8.3 8.2 8.3 8.2 8.4 8.4 8.3 8.2 8.3	167 196 190 187 149 141 160 190 175

a) What is the appropriate statistic?
---Select one--- (na, Correlation, Slope, Chi-Square)
Compute the option selected in a):  

b) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =  
Decision:  ---Select one--- (Reject H0, Fail to reject H0)

d) Make an interpretation based on the results.

a. More sodium intake significantly predicts an increase in blood pressure.

b. More sodium intake significantly predicts a decrease in blood pressure.

c. Sodium intake does not significantly predict blood pressure.

Answer 1

(a) The appropriate statistic is Correlation

To calculate pearsons co efficient r

From the data given, we get the following table and values

Count	x	y	xy	x2	y2
1	8.3	167	1386.1	68.89	27889
2	8.2	196	1607.2	67.24	38416
3	8.3	190	1577	68.89	36100
4	8.2	187	1533.4	67.24	34969
5	8.4	149	1251.6	70.56	22201
6	8.4	141	1184.4	70.56	19881
7	8.3	160	1328	68.89	25600
8	8.2	190	1558	67.24	36100
9	8.3	175	1452.5	68.89	30625
Total	74.6	1555	12878.2	618.4	271781

SUM (x) = 74.6, SUM (y) = 1555, SUM (xy) = 12878.2,

SUM (x²) = 618.4, (SUM x)² = (74.6)²= 5565.16

SUM (y²) = 271781, (SUM y)² = (1555)² = 2418025

SUM (x) x SUM (y) = 74.6 x 1555 = 116003

n = 9

r = -0.8937

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(b) The Hypothesis Test

The Hypothesis:

H0: = 0 : There is no linear relationship between the 2 variables.

Ha : 0 : There is a linear relationship between the 2 variables.

The Test Statistic:

The Critical Value (2 tail): at = 0.05, df = n -2 = 7 is -2.365 and +2.365

The Decision Rule: If T obtained is < -t critical or if t obtained is > t critical, then Reject H0.

The Decision: Since t obtained (-5.27) is < -t critical(-2.365), We Reject H0.

The Conclusion: There is sufficient evidence at the = 0.01 level to conclude that there is a linear relationship between the 2 variables (i.e r is significant).

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Interpretation. Since there is a significant relationship and the same is negative, therefore

Option b: More sodium intake significantly predicts a decrease in blood pressure.

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