Question

n a study designed to test the effectiveness of magnets for treating back​ pain, 3535 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 3535 patients had pain scores with a mean of 12.0 and a standard deviation of 2.2. After being given the sham​ treatments, the 3535 patients had pain scores with a mean of 10.2 and a standard deviation of 2.6

Construct the 90​% confidence interval estimate of the mean pain score for patients given the sham treatment.

What is the confidence interval estimate of the population mean μ​?

Answer 1

Solution :

Given that,

Point estimate = sample mean = =10.2

sample standard deviation = s = 2.6

sample size = n = 35

Degrees of freedom = df = n - 1 = 35-1 = 34

At 90% confidence level

= 1-0.90% =1-0.9 =0.10

/2 =0.10/ 2= 0.05

t/2,df = t_{0.05,34 = 1.69}

t _/2,df = 1.69

Margin of error = E = t_/2,df * (s /n)

= 1.69* ( 2.6/ 35)

Margin of error = E =0.743

The 90% confidence interval estimate of the population mean is,

- E < < + E

10.2-0.743 < < 10.2+0.743

9.457 < < 10.943

(9.457,10.943)