In a study designed to test the effectiveness of magnets for treating back pain,
ID: 3217143 • Letter: I
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 12.0 and a standard deviation of 2.3. After being given the sham treatments, the 35 patients had pain scores with a mean of 12.2 and a standard deviation of 2.5. Complete parts (a) through (c) below. Click here to view a t distribution table Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 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 H? (Round to one decimal place as needed.)Explanation / Answer
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=12
Standard deviation( sd1 )=2.3
Sample Size(n1)=35
Mean(x2)=12.2
Standard deviation( sd2 )=2.5
Sample Size(n2)=35
CI = [ ( 12-12.2) ±t a/2 * Sqrt( 5.29/35+6.25/35)]
= [ (-0.2) ± t a/2 * Sqrt( 0.3297) ]
= [ (-0.2) ± 2.032 * Sqrt( 0.3297) ]
= [-1.3668 , 0.9668]