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A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain

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Answer #1

Step 1:

\mu_{D} ≤ 0

\mu_{D} > 0

Step 2: Test statistics

employee Before After Diff (Bef-after) Dev (diff - mean) Sq deviation
1 7.8 6.4 1.4 -0.75 0.56
2 4.9 2.8 2.1 -0.05 0.00
3 9.9 7.7 2.2 0.05 0.00
4 12.0 8.6 3.4 1.25 1.56
5 9.2 8.4 0.8 -1.35 1.82
6 9.2 6.1 3.1 0.95 0.90
7 5.9 3.2 2.7 0.55 0.30
8 3.9 2.4 1.5 -0.65 0.42
Total 63 46 17.200 0.0000 5.5800

mean difference = 17.2 /8  = 2.15

sd difference = SD_{D}

SD_{D} = \sqrt{\frac{\sum (x - \Bar{x})^{2}}{n-1}} = \sqrt{\frac{5.58}{7}}

SD_{D} = 0.8928

t = \frac{\bar{x}_{D}}{\sqrt{SD_{D}/\sqrt{n}}} = \frac{2.15}{0.8928/\sqrt{8}}

t = 6.811

tc​ = 1.895, for α = 0.05 and df=7

As t stat falls in the rejection area, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that hypontism appears to be effective in reducing pain.

Confidence interval :

t value = TINV( 0.05, 7) = 2.365

E = 2.365 * (0.8928 / sqrt(8)) = 0.746

CI = 2.15 +/- 0.746

CI = 1.404 , 2.896

Correct option : B Yes, because the CI does not include zero and is entirely greater than zero.

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