Question

In a study designed to test the effectiveness of magnets for treating back pain, 35 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 35 patients had pain scores with a mean of 10.0 and a standard deviation of 2.2. After being given the sham treatments, the 35 patients had pain scores with a mean of 8.1 and a standard deviation of 2.5.

a) Construct the 95% confidence interval estimate of the mean pain score for patients given the magnet treatment.

What is the confidence interval estimate of the population mean?

___ < u < ___

b) Construct the 95% confidence interval estimate of the mean pain score for patients given the sham treatment.

What is the confidence interval estimate of the population mean?

___ < u < ____

c) Compare the results. Does the treatment with magnets appear to be effective?

Answer 1

The formula for estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

a) for magnet treatment

Calculation

M = 10
t = 1.96
s_M = √(2.2²/35) = 0.37

μ = M ± Z(s_M)
μ = 10 ± 1.96*0.37
μ = 10 ± 0.73

Result

M = 10, 95% CI [9.27, 10.73].

You can be 95% confident that the population mean (μ) falls between 9.27 and 10.73.

b)  Calculation for sham treatment

M = 8.1
t = 1.96
s_M = √(2.5²/35) = 0.42

μ = M ± Z(s_M)
μ = 8.1 ± 1.96*0.42
μ = 8.1 ± 0.828

Result

M = 8.1, 95% CI [7.272, 8.928].

You can be 95% confident that the population mean (μ) falls between 7.272 and 8.928

C)

Using two sample t test we get P value and statistical significance:
  The two-tailed P value equals 0.0012
  By conventional criteria, this difference is considered to be very statistically significant.

Since the p value is less than 0.05 then we have say that the treatments with magnet effective.