The 95% confidence interval estimate of the mean wake time is equal to (62.61, 88.39).
<u>Given the following data:</u>
- Mean wake time = 75.5 min.
- Standard deviation = 24.2 min.
- Number of sample, n = 16.
<h3>How to construct a 95% confidence interval?</h3>
Mathematically, a confidence interval of 95% is given by;
α = 1 - 0.95
α = 0.05.
α/2 = 0.05/2 = 0.025.
Also, the degrees of freedom (df) is given by:
Degrees of freedom (df) = n - 1
Degrees of freedom (df) = 16 - 1
Degrees of freedom (df) = 15.
From the Student's t-distribution table, a critical value at t₀.₀₂₅, ₁₅ = 2.131.
Mathematically, the confidence interval for mean is given by:
Mean ± (t-critical × (standard deviation/√(sample size)))
75.5 ± (2.131 × (24.2/√(16))
75.5 ± (2.131 × 6.05)
For the upper end, we have:
75.5 + 12.89 = 88.39
For the lower end, we have:
75.5 - 12.89 = 62.61.
In conclusion, we can deduce that there isn't a significant difference between the mean wake time before and after treatment and as such, this drug isn't effective at the significance level of 0.05.
Read more on confidence interval here: brainly.com/question/25779324
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