Question

Listed below is a simple random sample of systolic blood pressure measurements (mm Hg) taken from the right and left arms of seven people

Right arm 138 128 154 144 137 157 126

Left arm 179 173 167 125 173 146 158

Use a 0.04 significance level to test the claim that the blood pressure in the right arm is less than the blood pressure in the left arm. Test statistic?

Answer 1

Using Excel functions average and stdev,s we find the mean and standard deviation for the two samples

	n	Mean (M)	Variance (SS)	Standard Deviation (SD)
Right Arm BP	n1 = 7	M1 = 140.5714	SS1 = 141.9524	s1 = 11.9144
Left Arm BP	n2 = 7	M2 = 160.1429	SS2 = 362.1429	s2 = 19.0301

The null and alternative hypotheses are
Ho :  μ1 = μ2
Ha :  μ1 < μ2
where μ1 , μ2 are the population means for the right and left arm blood pressures respectively
α = 0.04            ...Level of significance

We use independent Samples T test since population standard deviation is unknown, and sample size is small
Using the given formulae, we get

Degrees of Freedom
df1 = n1 - 1 , df2 = n2 - 1 , df = n1 + n2 - 2

df = 12

Pooled Variance

Sp2 = 252.0476

Mean Squared Error Sm1-m2


Sm1-m2 = 8.4861

t-statistic

t-statistic = t = -2.3063


P-value
For t = -2.3063, df = 12 we find the one tailed p-value using t tables or Excel function t.dist
p-value = t.dist(-2.3063, 12, TRUE)
p-value = 0.0199


Decision
0.0199 < 0.04

that is p-value is less than alpha.
Hence we Reject Ho.

Conclusion
There exists enough statistical evidence at α = 0.04 to show that the blood pressure in the right arm is less than the blood pressure in the left arm.

If you are satisfied with the solution, kindly give a thumbs up.