Question

8. A clinical trial was conducted to test the effectiveness of the drug Zopiclone for treating insomnia in older subjects. Before treatment with Zopiclone, 16 subjects had a mean wake time of 102.8 minutes. After treatment with Zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and a standard deviation of 42.3 minutes. Assume that the sample values were collected from a normally distributed population. Test the claim that after treatment with Zopiclone, subjects have a mean wake time of less than 102.8 minutes at a = 0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 102.8
Alternative Hypothesis, Ha: μ < 102.8

Rejection Region
This is left tailed test, for α = 0.05 and df = 15
Critical value of t is -1.753.
Hence reject H0 if t < -1.753

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (98.9 - 102.8)/(42.3/sqrt(16))
t = -0.369

P-value Approach
P-value = 0.3586
As P-value >= 0.05, fail to reject null hypothesis.

No sufficient evidence