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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