Squatting for defecation continues to be the traditional position in most of Asi

Question

Squatting for defecation continues to be the traditional position in most of Asia and Africa. In contrast, sitting on toilet seats has proliferated in Western countries since the 19th century with the development of the sewage system. This difference, along with differences in diet, might explain the higher rate of hemorrhoids and constipation in Western countries. A recent study asked if body position affects defecation in humans. Researchers recruited 6 healthy adult volunteers and took X-rays of their intestinal systems to measure the anorectal angle (in degrees). Note that, as with a water hose, an angle of 180 degrees should provide the least amount of flow disruption. For each subject, an X-ray was taken once in a sitting position and once in a squatting position. Here are the findings:

Let

be the mean difference (squatting minus sitting).

(a) State the null and alternative hypotheses.

versus Ha:<0

versus Ha:>0

versus Ha:0

(b) Carry out a test at =0.01

:

df =

x¯¯¯

(±

0.001) =

t

(±

0.001) =

P

(±

0.0001) =

Conclusion:

NOTE: The numerical values in this problem have been modified for testing purposes.

Squatting for defecation continues to be the traditional position in most of Asia and Africa. In contrast, sitting on toilet seats has proliferated in Western countries since the 19th century with the development of the sewage system. This difference, along with differences in diet, might explain the higher rate of hemorrhoids and constipation in Western countries. A recent study asked if body position affects defecation in humans. Researchers recruited 6 healthy adult volunteers and took X-rays of their intestinal systems to measure the anorectal angle (in degrees). Note that, as with a water hose, an angle of 180 degrees should provide the least amount of flow disruption. For each subject, an X-ray was taken once in a sitting position and once in a squatting position. Here are the findings:

Subject Sitting Squatting 1 110 121 2 74 126 3 115 141 4 77 105 5 98 121 6 127 140

Let

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Squatting and Sitting
H0 : D = 0
HA : D 0
Hypothesis test results:

Hence,

a) H0: =0

versus Ha:0

Option C is correct.

b) Df = 5

t = 4.247

P value = 0.0081

Conclusion: This is significant at =0.01

Difference Mean Std. Err. DF T-Stat P-value Squatting - Sitting 25.5 6.0041652 5 4.2470517 0.0081

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