Question

A
clinical trial was conducted to test the effectiveness of a drug
for treating insomnia in older subjects. Before treatment, 25
subjects had a mean wake time of 103.0 min. After treatment, the 25
subjects had a mean wake time of 96.1 min and a standard deviation
of 22.8 min. Assume thay the 25 sample values appear to be from a
normally distrubuted population and construct a 95% confidence
interval estimate of the mean wake time for a population with drug
treatments. What does the result suggest about the mean wake time
of 103.0 min before the treatment? Does the drug appear to be
effective?

Answer #1

Solution :

Given that,

Point estimate = sample mean = = 96.1 min.

sample standard deviation = s = 22.8 min.

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2
= 0.025

t/2,df
= t0.025,24 = 2.064

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

= 2.064 * (22.8 / 25)

Margin of error = E = 9.4

The 95% confidence interval estimate of the population mean is,

- E < < + E

96.1 - 9.4 < < 96.1 + 9.4

86.7 min. < < 105.5 min.

The confidence interval include the mean wake time of 103.0 min.before the treatment so the means before and after the treatment are same this result suggests that the drug treatment does not have a significant effect

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