Question

A researcher wanted to see if high doses of cinnamon could lower hemoglobin A1c levels in prediabetic patients. A1c levels were measured in 8 randomly selected subjects before they began a treatment plan involving cinnamon supplements. Then their A1c levels were measured again 6 months after they had been adhering to the supplementation. Here is the data. Does the cinnamon supplement appear to be effective in lowering the A1c levels? Test the claim at the 1% significance level.

Subject	A	B	C	D	E	F	G	H
A1C Before	6.4	5.7	5.8	5..8	5.9	6.4	6.2	6.1
A1C After	6.3	5.6	5.5	5.3	5.9	6.5	6.0	5.9

Answer 1

Step 1:

Ho : = 0

Ha:

Step 2: T test for paired samples:

n = 8

Patient	Before	After	Diff (Af-Bef)
A	6.4	6.3	-0.1
B	5.7	5.6	-0.1
C	5.8	5.5	-0.3
D	5.8	5.3	-0.5
E	5.9	5.9	0
F	6.4	6.5	0.1
G	6.2	6	-0.2
H	6.1	5.9	-0.2
Total	48.3	47	-1.3

=  sum. of diff / no of terms = -1.3/ 8 = -0.1625

Standard deviaiton of the differences = SDD

data	data-mean	(data - mean)2
-0.1	0.0625	0.00390625
-0.1	0.0625	0.00390625
-0.3	-0.1375	0.01890625
-0.5	-0.3375	0.11390625
0	0.1625	0.02640625
0.1	0.2625	0.06890625
-0.2	-0.0375	0.00140625
-0.2	-0.0375	0.00140625

SDD = 0.1847

Step 3:

df = 7, = 0.01

t critical for lest tailed test = - 2.998

As the t stat (-2.488) does not fall in the rejection area, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that the cinnamon supplement is effective in lowering the A1c levels.