Math Problem Statement
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 13 subjects had a mean wake time of 100.0 min. After treatment, the 13 subjects had a mean wake time of 71.7 min and a standard deviation of 24.3 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 99% 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 100.0 min before the treatment? Does the drug appear to be effective?Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment.
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Interval
Hypothesis Testing
Formulas
Confidence Interval for Mean: CI = X̄ ± Z * (σ/√n)
Standard Error of Mean: SE = σ/√n
Theorems
Central Limit Theorem
Z-distribution for Confidence Intervals
Suitable Grade Level
Grades 11-12 or College Level
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