A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug, 29 subjects had a mean wake time of 98.2 minutes and a standard deviation of 43.4 minutes. Assume that the 29 sample values appear to be from a normally distributed population.

Construct a 95% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is effective?

Find the confidence interval estimate:

[min] < [tex]\sigma[/tex] < [min]

(Round to two decimal places as needed.)

The confidence interval for the standard deviation of wake times with the drug treatment, at a 95% confidence level, is calculated as 31.36 min to 64.53 min. This indicates that we are 95% confident that the true standard deviation of wake times for the population receiving the drug falls within this range.

This result alone does not provide information about whether the treatment is effective for insomnia in older subjects. Confidence intervals for the standard deviation provide insights into the variability of the data but do not assess treatment effectiveness directly. To determine if the treatment is effective, further analysis, such as comparing pre- and post-treatment wake times or conducting hypothesis tests, would be needed.

In summary, while we have estimated the standard deviation with confidence, additional statistical analysis is required to assess the effectiveness of the drug in treating insomnia in older subjects.

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