Question

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the​ drug, 23 subjects had a mean wake time of 92.7 min and a standard deviation of 40.3 min. Assume that the 23 sample values appear to be from a normally distributed population and construct a 90​% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is​ effective?

I got 32.45 < o < 53.82
is this right? and what is the mc answer if so.

Does the result indicate whether the treatment is​ effective?

A.

​Yes, the confidence interval indicates that the treatment is not effective because the interval does not contain 0 minutes.

B.

​Yes, the confidence interval indicates that the treatment is not effective because the interval contains 0 minutes.

C.

​Yes, the confidence interval indicates that the treatment is effective because the interval does not contain 0 minutes.

D.​Yes, the confidence interval indicates that the treatment is effective because the interval does not contain

92.792.7

minutes.

E.

​Yes, the confidence interval indicates that the treatment is effective because the interval contains 0 minutes.

F.​Yes, the confidence interval indicates that the treatment is not effective because the interval does not contain

92.792.7

minutes.

G.

​No, the confidence interval does not indicate whether the treatment is effective.

Answer 1

CONFIDENCE INTERVAL FOR STANDARD DEVIATION
ci = (n-1) s^2 / ᴪ^2 right < σ^2 < (n-1) s^2 / ᴪ^2 left
where,
s = standard deviation
ᴪ^2 right = (1 - confidence level)/2
ᴪ^2 left = 1 - ᴪ^2 right
n = sample size
since alpha =0.1
ᴪ^2 right = (1 - confidence level)/2 = (1 - 0.9)/2 = 0.1/2 = 0.05
ᴪ^2 left = 1 - ᴪ^2 right = 1 - 0.05 = 0.95
the two critical values ᴪ^2 left, ᴪ^2 right at 22 df are 33.9244 , 12.338
s.d( s )=40.3
sample size(n)=23
confidence interval for σ^2= [ 22 * 1624.09/33.9244 < σ^2 < 22 * 1624.09/12.338 ]
= [ 35729.98/33.9244 < σ^2 < 35729.98/12.338 ]
[ 1053.2236 < σ^2 < 2895.9296 ]
and confidence interval for σ = sqrt(lower) < σ < sqrt(upper)
= [ sqrt (1053.2236) < σ < sqrt(2895.9296), ]
= [ 32.4534 < σ < 53.8138 ]
90​% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments
[ 32.4534 < σ < 53.8138 ]
the treatment is​ effective,
option :C
yes,
the confidence interval indicates that the treatment is effective because the interval does not contain 0 minutes.
D.​
Yes, the confidence interval indicates that the treatment is effective because the interval does not contain 92.792.7 minutes.