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