Question

(Please describe each solution step in detail.)

In a study designed to test the effectiveness of magnets for treating back pain ,40 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale from 0 (no pain) to 100 (extreme pain) . After given the magnet treatments, the 40 patients had pain scores with a mean of 12.0 and a standard deviation of 2.1. After being given the sham treatment the 40 patients had pain scores with a mean of 10.4 and a standard deviation of 2.5.

a- construct the 95% confidence interval estimate of the mean pain scores for patients given the magnet treatment.

Answer 1

a)
Given
X̅ = 12           ....... Sample Mean
n = 40           ....... Sample Size
s = 2.1           ....... Sample Standard Deviation

Since the population standard deviation is unknown, we use the t-distribution

Degrees of Freedom = df = n - 1 = 40 - 1 = 39

For 95% Confidence interval

α = 0.05,      α/2 = 0.025
From t tables of Excel function T.INV.2T (α, degrees of freedom) we find the t value
t = T.INV.2T (0.05, 39) = 2.023
We take the positive value of t

Confidence interval is given by


= (11.3283, 12.6717)

95% Confidence interval is estimate of the mean pain scores for patients given the magnet treatment

OR after rounding to 1 decimal place

95% Confidence interval is estimate of the mean pain scores for patients given the magnet treatment

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