Magnets for treating back pain Here the population Std Dev I

Magnets for treating back pain: (Here the population Std. Dev. Is unknown) in a study designed to test the effectiveness of magnets for treating back pain, 20 patients were given a treatment with magnets and also a sharm treatments, the 20 patients had VAS scores with a mean 5.0 and a standard deviation of 2.4. After given the magnet treatments, the 20 patients had VAS scores with a mean of 4.7 and a standard deviation 2.9 Construct the 95% confidence interval estimate of mean VAR score for patients given the magnet treatment. Construct a 95% confidence interval estimate of the mean VAS score for patients given a sharm treatment. Compare the results. Does the treatment with magnets appear to be effective?

Solution

a)
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=5
Standard deviation( sd )=2.4
Sample Size(n)=20
Confidence Interval = [ 5 ± t a/2 ( 2.4/ Sqrt ( 20) ) ]
= [ 5 - 2.093 * (0.537) , 5 + 2.093 * (0.537) ]
= [ 3.877,6.123 ]
b)
Mean(x)=4.7
Standard deviation( sd )=2.9
Sample Size(n)=20
Confidence Interval = [ 4.7 ± t a/2 ( 2.9/ Sqrt ( 20) ) ]
= [ 4.7 - 2.093 * (0.648) , 4.7 + 2.093 * (0.648) ]
= [ 3.343,6.057 ]

c)
Treatment with Magenet be efctive as the upper interval of magnet is above the sham treatment