An experiment was performed to see whether sensory deprivation over an extended

Question

An experiment was performed to see whether sensory deprivation over an extended period of
time has any effect on the alpha-wave patterns produced by the brain. To determine this, 10
subjects, inmates in a Canadian prison, were randomly split onto two groups. Members of one
group were placed in solitary confinement. Those in the other group were allowed to remain
in their own cells. Seven days later, alpha-wave frequencies were measured for all subjects,
as shown in the following table. Assume the normal distribution. Construct 95% confidence
interval for the mean difference.

Nonconfined 10.7   10.7   10.4 10.9 10.5
Confined         9.7   10.3     9.2    9.3     9.9

Explanation / Answer

Nonconfined: xbar1=10.64, s1=0.19, n1=5
Confined: xbar2=9.68, s2=0.45, n2=5

Given a=0.05, |t(0.025, df=n1+n2-2=8)|=2.31 (check student t table)

So the 95% CI is
(xbar1 -xbar2) ± t*[s1^2/n1 + s2^2/n2]

--> (10.64 - 9.68) ± 2.31*sqrt(0.19^2/5 + 0.45^2/5)

--> ( 0.455, 1.464)

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