Question

A food company has developed a high mineral sea salt (sodium). A nurse practitioner wants to know if blood pressure can be predicted from the sodium intake of the new sea salt. 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 α = 0.01?

Sodium	BP
8.3 8.2 8.3 8.2 8.4 8.4 8.3 8.2 8.3	167 146 190 187 149 141 145 190 175

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected a):

b) Compute the appropriate test statistic(s) 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--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

More sodium intake significantly predicts an increase in blood pressure.More sodium intake significantly predicts a decrease in blood pressure.    Sodium intake does not significantly predict blood pressure.

Answer 1

X	Y	XY	X²	Y²
8.3	167	1386.1	68.89	27889
8.2	146	1197.2	67.24	21316
8.3	190	1577	68.89	36100
8.2	187	1533.4	67.24	34969
8.4	149	1251.6	70.56	22201
8.4	141	1184.4	70.56	19881
8.3	145	1203.5	68.89	21025
8.2	190	1558	67.24	36100
8.3	175	1452.5	68.89	30625
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
74.6	1490	12343.7	618.4	250106

Sample size, n =	9
x̅ = Ʃx/n = 74.6/9 =	8.28888889
y̅ = Ʃy/n = 1490/9 =	165.555556
SSxx = Ʃx² - (Ʃx)²/n = 618.4 - (74.6)²/9 =	0.04888889
SSyy = Ʃy² - (Ʃy)²/n = 250106 - (1490)²/9 =	3428.22222
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 12343.7 - (74.6)(1490)/9 =	-6.74444444

a) Appropriate test statistic : Correlation

b) Null and alternative hypothesis:

Ho: ρ = 0 ; Ha: ρ < 0

α = 0.01

df = n-2 = 7

Critical value, t_c = ABS(T.INV(0.01, 7)) = -2.9980

Test statistic :  

t = r*√(n-2)/√(1-r²) = -0.521 *√(9 - 2)/√(1 - -0.521²) = -1.6148

Fail to reject H0

c) Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy) = (-6.74444)²/(0.04889*3428.22222) = 0.2714

small effect

d) Sodium intake does not significantly predict blood pressure.