Question

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval for the mean of the "before−after" differences. Does hypnotism appear to be effective in reducing pain? In this example, μd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the difference in the measurements in centimeters on a pain scale before and after hypnosis. What is the P-value for this hypothesis test? (Round to three decimal places as needed.) Answer

Answer 1

Required data:

Before 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

After 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

Answer:

Confidence interval = (-0.404 ; 1.804)

Pvalue = 0.178

Explanation:

H0: μd = 0

H1 : μd ≠ 0

Difference, d = (x - y)

d = - 0.3, 0.2, 0.3, 2.4, 3.1, - 0.6, 0.4, 0.1

Using calculator :

μd = 0.7

Sd = 1.32

Confidence interval :

Mean ± margin of error

Margin of Error =Tcritical * Sd/√n

Tcritical at df = 7, 0.5, 2 - tailed = 2.365

Margin of Error = 2.365 * 1.32/√8

Margin of Error = 1.104

Lower boundary :

(0.7 - 1.104) = - 0.404

Upper boundary :

(0.7 + 1.104) = 1.804

(-0.404 ; 1.804)

Test statistic, = μd / (Sd ÷ √n)

Test statistic = 0.7 / (1.32 ÷ √8)

Test statistic = 1.499

From the test statistic score ; using a Pvalue calculator :

Pvalue = 0.178 ( 3 decimal places)